Measuring: Choosing Instruments and Units, Reading Scales and Accuracy

October 28, 2026October 28, 2026 Aven Brisail1 Comment

FORM 2 • TERM 2 • LESSON 20

Measuring is everywhere: a tailor measuring cloth for a school uniform, a vendor weighing tomatoes at the market, a nurse taking your temperature, or a teacher timing the 100 m on Sports Day. In Form 1 you learned the units of measurement and about mass and weight. In Lesson 4 you rounded and estimated. In this lesson you will choose the right instrument and unit for a job, read scales carefully, and say how accurate a measurement is.

Learning outcomes

By the end of this lesson you should be able to:

2.5.1.1 – Choose a suitable measuring instrument for a quantity.
2.5.1.2 – Choose the most suitable unit for measuring a quantity.
2.5.1.3 – Read and make sense of scales on measuring instruments.
2.5.1.4 – Measure quantities to a stated degree of accuracy, including time on the 24-hour clock.

Choosing a measuring instrument

Different jobs need different tools. For length alone there are several instruments, depending on how long the object is and how accurate you need to be.

Instrument	Measures, for example
Ruler or metre rule	Short lengths: a pencil, a page
Tape measure	Longer lengths: a room, your waist
Trundle wheel	Long distances: the school field
Vernier caliper	Small lengths: the width of a pipe
Micrometer screw gauge	Very small lengths: the thickness of a wire
Scale or balance	Mass: flour, a bag of rice, you
Measuring cylinder or jug	Capacity: medicine, water for cooking
Thermometer	Temperature: body or air temperature
Clock or stopwatch	Time: a race, a class period
Protractor	Angle: an angle in a triangle

A trundle wheel clicks once for every metre it rolls, so you count the clicks. A vernier caliper and a micrometer screw gauge are used in the science lab for lengths much smaller than a ruler can measure well.

Choosing the best unit

Choose a unit that gives a sensible number, not a huge one or a tiny decimal. You would give the length of your exercise book in centimetres, not kilometres!

Quantity	Units (small to large)	Example
Length	mm, cm, m, km	Coin thickness: mm. Door height: m.
Mass	mg, g, kg, tonne	A mango: g. A bag of rice: kg.
Capacity	ml, l	A spoon of medicine: ml. A bucket: l.
Temperature	°C	A hot day: about 32 °C.
Time	s, min, h	A sprint: s. A football match: min.

Reading a scale

Most scales have only some marks labelled. To read a scale:

Find two labelled marks next to each other, for example 30 and 40.
Count the spaces (not the lines) between them, for example 5.
Work out the value of one division: difference ÷ number of spaces. Here (40 − 30) ÷ 5 = 2.
Count the divisions from the labelled mark just below the reading, and add.

Figure 1 – Each small division on this ruler is 1 mm (0.1 cm). The bar starts at 2.0 cm and ends at 9.4 cm, so its length is 9.4 − 2.0 = 7.4 cm.

When you measure with a ruler, line the start of the object up with the 0 mark if you can. If you start at another mark, as in Figure 1, subtract: end reading − start reading.

Figure 2 – On this measuring cylinder there are 5 spaces between 30 ml and 40 ml, so each division is 2 ml. Read the bottom of the curved surface (the meniscus) with your eye level with it: 34 ml.

Water in a narrow tube curves at the top. This curve is the meniscus. Read the bottom of the curve, with your eye level with the surface. If you look from above or below, the reading will be wrong. This error is called parallax.

Figure 3 – This thermometer has 5 spaces between 30 °C and 40 °C, so each division is 2 °C. The liquid is 1 division above 30, so the temperature is 32 °C.

Degree of accuracy

No measurement is exact. The smallest division on the scale limits how accurate you can be. A ruler marked in millimetres measures to the nearest millimetre (0.1 cm). A kitchen scale marked every 20 g measures to the nearest 20 g, or perhaps the nearest 10 g if you judge halfway.

When a measurement is rounded, the true value can be up to half a unit either side. The bar in Figure 1 is 7.4 cm to the nearest 0.1 cm, so its true length is from 7.35 cm up to (but not including) 7.45 cm. This is the same idea as rounding in Lesson 4.

Value	Accurate to	True value lies
15 cm	nearest cm	14.5 cm to 15.5 cm
7.4 cm	nearest 0.1 cm	7.35 cm to 7.45 cm
250 g	nearest 10 g	245 g to 255 g
3 h	nearest hour	2.5 h to 3.5 h

Time and the 24-hour clock

Bus and ferry timetables, airline tickets and phones often use the 24-hour clock. It always uses four digits, and there is no a.m. or p.m.

For a.m. times, write the time with four digits: 7:05 a.m. is 07:05. Midnight is 00:00.
For p.m. times from 1:00 p.m. on, add 12 to the hours: 2:45 p.m. is 14:45. Noon is 12:00.
To find how long something takes, count on to the next hour, then on to the end time.

Worked examples

Example 1: Instrument and unit

Question: Choose an instrument and a unit for measuring
(a) the thickness of a $1 coin
(b) the length of the school corridor
(c) the mass of a bag of rice.

A coin is very thin, so use a small, accurate instrument and a small unit.
A corridor is long, so use something that measures long lengths.
A bag of rice is heavy compared with a mango, so use kilograms.

Answer:
(a) vernier caliper, mm
(b) tape measure or trundle wheel, m
(c) scale, kg

Example 2: Reading a kitchen scale

Question: A kitchen scale is labelled 0, 100, 200, 300 g with 5 spaces between labels. The pointer is 3 divisions past 200. What is the mass?

Value of one division: 100 ÷ 5 = 20 g.
Reading: 200 + 3 × 20 = 260 g.

Answer: 260 g.

Example 3: Reading a measuring cylinder

Question: Use Figure 2. What volume of water is in the cylinder?

There are 5 spaces between 30 ml and 40 ml, so each division is (40 − 30) ÷ 5 = 2 ml.
The bottom of the meniscus is 2 divisions above 30.
30 + 2 × 2 = 34.

Answer: 34 ml.

Example 4: Limits of accuracy

Question: A piece of ribbon is 12.6 cm long, measured to the nearest millimetre. Between which values does its true length lie?

The nearest millimetre is the nearest 0.1 cm. Half of 0.1 cm is 0.05 cm.
12.6 − 0.05 = 12.55 and 12.6 + 0.05 = 12.65.

Answer: from 12.55 cm up to 12.65 cm.

Example 5: A maxi-taxi journey

Question: A maxi-taxi leaves at 2:50 p.m. and arrives at 4:15 p.m.
(a) Write both times in the 24-hour clock.
(b) How long is the journey?

2:50 p.m. is 14:50 and 4:15 p.m. is 16:15.
From 14:50 to 15:00 is 10 minutes. From 15:00 to 16:15 is 1 hour 15 minutes.
10 minutes + 1 hour 15 minutes = 1 hour 25 minutes.

Answer:
(a) 14:50 and 16:15
(b) 1 hour 25 minutes

Common mistakes

Counting lines instead of spaces. Between 30 and 40 with 4 small lines in between there are 5 spaces, so each is worth 2, not 2.5.
Starting the ruler at its edge. Many rulers have a gap before 0. Start at the 0 mark, or subtract the start reading.
Reading the meniscus from above. Keep your eye level with the bottom of the curve.
Using a silly unit. The mass of a pencil in kilograms gives a tiny decimal; use grams.
24-hour clock slips. 15:00 is 3:00 p.m., not 5:00 p.m. Subtract 12 from the hours after noon.

Practice questions

Try these yourself first, then open each answer to check your working.

1. Which instrument is best for measuring the diameter of a thin copper wire?
A. A metre rule
B. A tape measure
C. A micrometer screw gauge
D. A trundle wheel

Show answer

C. A micrometer screw gauge measures very small lengths, to about 0.01 mm.

2. Choose the best unit for each.
(a) The mass of an egg
(b) The length of a cricket pitch
(c) The capacity of a teaspoon
(d) The distance from Port of Spain to Arima

Show answer

(a) grams (g)
(b) metres (m)
(c) millilitres (ml)
(d) kilometres (km)

3. A scale is labelled 0, 10, 20, … with 5 equal spaces between each pair of labels. The pointer is 3 small divisions past 10. What is the reading?

Show answer

Each division is 10 ÷ 5 = 2. The reading is 10 + 3 × 2 = 16.

4. A measuring jug is labelled every 100 ml, with 4 spaces between labels. The juice is 2 divisions above the 300 ml mark. How much juice is in the jug?

Show answer

Each division is 100 ÷ 4 = 25 ml. The amount is 300 + 2 × 25 = 350 ml.

5. A leaf is placed on a ruler. One end is at 3.0 cm and the other end is at 11.7 cm. How long is the leaf, in cm and in mm?

Show answer

11.7 − 3.0 = 8.7 cm, which is 87 mm.

6. A bag of flour has a mass of 25 kg, correct to the nearest kilogram. Between which two values does its true mass lie?

Show answer

Between 24.5 kg and 25.5 kg (half of 1 kg either side).

7. On the thermometer in Figure 3, the liquid drops to 3 divisions above the 20 °C mark. What is the temperature now?

Show answer

Each division is 2 °C, so the temperature is 20 + 3 × 2 = 26 °C.

8. Write each time in the 24-hour clock.
(a) 7:05 a.m.
(b) 9:40 p.m.
(c) Write 00:15 in the 12-hour clock.

Show answer

(a) 07:05
(b) 21:40
(c) 12:15 a.m. (a quarter past midnight)

9. On Sports Day, Kemba ran 100 m in 12.4 seconds, timed to the nearest tenth of a second. What are the shortest and longest times she could really have taken?

Show answer

From 12.35 s up to 12.45 s. The time is within half of 0.1 s, which is 0.05 s, of 12.4 s.

Quick check

1. On a ruler marked in millimetres, what is each small division worth in centimetres?

Show answer

0.1 cm (1 mm).

2. Where do you read the level of water in a measuring cylinder?

Show answer

At the bottom of the curved surface (the meniscus), with your eye level with it.

3. What is 18:00 in the 12-hour clock?

Show answer

6:00 p.m.

Previous: Reflections in Horizontal and Vertical Mirror Lines on a Coordinate Grid

Next: Converting Units: Metric Units, Metric and Imperial, and Area Units

Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 2, Term 2, Strand 2.5 Measurement, Topic 2.5.1 Units of Measurement and Conversion of Units – Learning Outcomes 2.5.1.1 (choosing measuring instruments), 2.5.1.2 (choosing suitable units), 2.5.1.3 (reading and interpreting scales) and 2.5.1.4 (measuring to a given degree of accuracy).

Updates

2026/10/28

– First version of this lesson.

Significant Figures, Estimation and Mental Maths Strategies

October 24, 2026October 25, 2026 Aven Brisail2 Comments

FORM 2 • TERM 1 • LESSON 04

In Form 1 you rounded numbers to the nearest 10, 100 or 1,000 and to a number of decimal places. This lesson adds a new way to round – to a number of significant figures – and shows how rounding helps you estimate quantities and check answers. You will also practise some mental maths strategies that make calculating in your head quicker.

Learning outcomes

By the end of this lesson you should be able to:

2.1.2.3 – Write numbers correct to a given number of significant figures (scientific notation and standard form follow in the next lesson).
2.1.2.4 – Estimate quantities and answers to calculations.
2.1.2.6 – Use mental maths strategies to calculate quickly.

What are significant figures?

The significant figures (s.f.) of a number are the digits that tell you how big it is, starting from the first non-zero digit. The first significant figure is the most important one, the second is the next most important, and so on.

Non-zero digits are always significant. 4,732 has 4 significant figures.
Zeros between non-zero digits are significant. 3,009 and 20.5 have 4 and 3 significant figures.
Zeros at the start of a decimal are not significant – they only show the place value. 0.0047 has 2 significant figures (4 and 7).
Zeros at the end of a decimal are significant. 2.50 has 3 significant figures: the last 0 tells you the value was measured to the nearest hundredth.
Zeros at the end of a whole number are usually place holders. In this course, 4,500 is treated as having 2 significant figures unless you are told it is exact.

Number	Significant figures	How many?
8,316	8, 3, 1, 6	4
507	5, 0, 7	3
0.0062	6, 2	2
0.0400	4, 0, 0	3
93,000	9, 3	2

Rounding to significant figures

Rounding to significant figures works just like rounding to decimal places, but you count from the first non-zero digit:

Count along from the first non-zero digit to the last significant figure you want to keep.
Look at the next digit (the decider). If it is 5 or more, round up; if it is 4 or less, leave the digit alone.
For a whole number, replace the digits you drop with zeros so the number keeps its size. For a decimal, simply drop the digits after the last one you keep.

So 34,567 to 2 s.f. is 35,000 (not 35), and 0.004072 to 3 s.f. is 0.00407. Significant figures are useful because they work for any size of number, and newspapers, scientists and engineers use them all the time.

TRY ITRound to significant figures

Type any number (a whole number or a decimal, with or without commas) and choose how many significant figures to round it to. The steps show which digit decides the rounding.

Number:

Significant figures:

Estimating answers

To estimate the answer to a calculation, round every number to 1 significant figure and work with the easy numbers. An estimate tells you roughly what the answer should be, so you can spot a calculator slip.

48.7 × 21.3 ≈ 50 × 20 = 1,000. (The exact answer is 1,037.31, so the estimate is close.)
612 ÷ 29 ≈ 600 ÷ 30 = 20.
(7.8 + 3.1) × 0.52 ≈ (8 + 3) × 0.5 = 5.5.

Use the symbol ≈, which means “is approximately equal to”, for an estimate.

Estimating quantities

Estimation is also how people find large numbers that are too slow to count, such as the crowd at a cricket match or the number of seeds in a bag. The idea is to count a small part and multiply.

For example, if one block of seats holds about 38 people across and 12 rows deep, it holds roughly 40 × 10 = 400 people. If the stand has 9 blocks like it, the stand holds about 400 × 9 = 3,600 people. In real life you choose sensible rounding: when shopping you might round up each price so you are sure to have enough money.

Mental maths strategies

Strategy	How it works	Example
Make a ten or a hundred	Round one number to a friendly one, then adjust	99 + 46 = 100 + 46 − 1 = 145
Split the number (distributive law)	Break a number into tens and units	7 × 36 = 7 × 30 + 7 × 6 = 210 + 42 = 252
Double and halve	Halve one number and double the other	25 × 16 = 50 × 8 = 100 × 4 = 400
Multiply by 5	Multiply by 10, then halve	68 × 5 = 680 ÷ 2 = 340
Count up to subtract	Count on from the smaller number	100 − 63.75: 63.75 → 64 → 100 is 0.25 + 36 = 36.25
Multiply by 9 or 11	Multiply by 10, then subtract or add one more	23 × 9 = 230 − 23 = 207

These strategies use the laws of numbers from the last lesson. You do not need all of them – pick the ones that suit the numbers in front of you.

Worked examples

Example 1: Counting significant figures

Question: How many significant figures are in
(a) 6,040
(b) 0.00719
(c) 12.80?

(a) Start at 6: the digits 6, 0, 4 count (the final 0 is a place holder), so 3 s.f.
(b) The leading zeros do not count: 7, 1, 9 gives 3 s.f.
(c) The final zero in a decimal counts: 1, 2, 8, 0 gives 4 s.f.

Answer:
(a) 3
(b) 3
(c) 4.

Example 2: Rounding a whole number

Question: Round 1,849,500 to
(a) 1 s.f.
(b) 3 s.f.

(a) The first figure is 1 (millions). The next digit is 8, so round up to 2,000,000.
(b) Keep 1, 8, 4. The next digit is 9, so round up to 185 and fill with zeros: 1,850,000.

Answer:
(a) 2,000,000
(b) 1,850,000.

Example 3: Rounding a small decimal

Question: Round 0.0050638 to 2 s.f.

The first non-zero digit is 5. Keep 5 and 0.
The next digit is 6, so round up: 0.0051.

Answer: 0.0051.

Example 4: Rounding up past a 9

Question: Round 6.996 to 3 s.f.

Keep 6, 9, 9. The next digit is 6, so the last 9 rounds up.
6.99 becomes 7.00. Keep the zeros to show 3 s.f.

Answer: 7.00.

Example 5: Estimating a calculation

Question: Estimate
(a) 387 × 52
(b) 8.9 × 4.1 ÷ 1.9.

(a) 387 ≈ 400 and 52 ≈ 50, so 400 × 50 = 20,000.
(b) 9 × 4 ÷ 2 = 36 ÷ 2 = 18.

Answer:
(a) about 20,000 (exact 20,124)
(b) about 18 (exact 19.2…).

Example 6: Estimating a shopping bill

Question: Kayla buys a shirt for $42.50, a bag of rice for $19.95 and juice for $7.85. Estimate the total. Will $80 be enough?

Round each price to 1 s.f.: $40, $20 and $8.
40 + 20 + 8 = 68.
The estimate is well under $80. (Exact total: $70.30.)

Answer: About $68, so $80 is enough.

Example 7: Mental maths

Question: Work out in your head:
(a) 198 + 375
(b) 35 × 12
(c) 5 × 84.

(a) 200 + 375 − 2 = 573.
(b) Halve and double: 70 × 6 = 420.
(c) 840 ÷ 2 = 420.

Answer:
(a) 573
(b) 420
(c) 420.

Common mistakes

Counting the leading zeros of a decimal. 0.0062 has 2 significant figures, not 5.
Forgetting the place-holder zeros. 34,567 to 2 s.f. is 35,000, not 35 – the answer must stay about the same size.
Dropping a zero you need. 6.996 to 3 s.f. is 7.00, not 7.
Mixing up decimal places and significant figures. 0.04072 to 2 d.p. is 0.04, but to 2 s.f. it is 0.041.
Estimating with numbers that are still hard. Round to 1 s.f. so that the calculation is easy in your head.

Practice questions

Try these yourself first, then open each answer to check your working.

1. How many significant figures are in:
(a) 2,705
(b) 0.083
(c) 5.00
(d) 70,000?

Show answer

(a) 4
(b) 2
(c) 3
(d) 1.

2. Round 58,362 to
(a) 1 s.f.
(b) 2 s.f.
(c) 3 s.f.

Show answer

(a) 60,000
(b) 58,000
(c) 58,400.

3. Round to 2 s.f.:
(a) 0.0738
(b) 4.951
(c) 0.0009962.

Show answer

(a) 0.074
(b) 5.0
(c) 0.0010.

4. Round 3.14159 to
(a) 1 s.f.
(b) 3 s.f.
(c) 4 s.f.

Show answer

(a) 3
(b) 3.14
(c) 3.142.

5. Estimate by rounding each number to 1 s.f.:
(a) 69 × 31
(b) 4,180 ÷ 19
(c) 0.48 × 210.

Show answer

(a) 70 × 30 = 2,100
(b) 4,000 ÷ 20 = 200
(c) 0.5 × 200 = 100.

6. A bus carries 48 passengers. About how many people can 22 buses carry?

Show answer

50 × 20 = 1,000, so about 1,000 people (exact 1,056).

7. Work out mentally:
(a) 299 + 467
(b) 8 × 47
(c) 15 × 14
(d) 1,000 − 386.

Show answer

(a) 300 + 467 − 1 = 766
(b) 320 + 56 = 376
(c) 30 × 7 = 210
(d) count up from 386: 14 + 600 = 614.

8. A section of a stand has 18 rows with 42 people in each row. Estimate the number of people, then work out the exact number.

Show answer

Estimate 20 × 40 = 800. Exact: 18 × 42 = 756.

Quick check

1. How many significant figures are in 0.0305?

Show answer

2. Round 7,482 to 1 s.f.

Show answer

7,000.

3. What does the symbol ≈ mean?

Show answer

Is approximately equal to.

Previous: Laws of Numbers: Commutative, Associative and Distributive Laws, Closure, Identity and Inverse

Next: Index Form, Standard Form and Scientific Notation (Positive Powers)

Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 2, Term 1, Strand 2.1 Number Operations and Number Theory, Topic 2.1.2 Laws and Properties of Numbers – Learning Outcomes 2.1.2.3 (writing numbers to a given number of significant figures), 2.1.2.4 (estimation) and 2.1.2.6 (mental maths strategies).

Attributions to media used in this post:

Dhaka stadium cricket Crowd.jpg – Wanoola – CC BY 2.0 (via Wikimedia Commons)

Updates

2026/10/23

– First version of this lesson.

2026/10/25

– Put each lettered part of the questions and answers on its own line.

Rounding Whole Numbers and Estimating Quantities (Nearest 10, 100, 1,000 and Million)

October 4, 2026 Aven BrisailLeave a comment

Rounding means replacing a number with a simpler, “rounder” number that is close to it. A newspaper might say a stadium held “about 27,000 people” when the exact count was 27,465. Rounded numbers are easier to remember, say and calculate with. Estimating means making a sensible guess at a quantity or an answer without counting or calculating everything exactly. In this lesson you will round whole numbers to the nearest 10, 100, 1,000 and up to the nearest million, and use benchmarks such as 100 to estimate large quantities.

You will need to be confident with place value first – see Place Value and Number Names.

The rounding rule

Find the rounding place (for example the hundreds digit if you are rounding to the nearest 100).
Look at the digit immediately to its right – this is the “decider” digit.
If the decider is 5, 6, 7, 8 or 9, round up: add 1 to the rounding digit.
If the decider is 0, 1, 2, 3 or 4, round down: leave the rounding digit as it is.
Replace every digit to the right of the rounding place with 0. Digits to the left do not change (unless rounding up turns a 9 into 10 – then carry, just like in addition).

Why does 5 round up? A number ending in exactly 5 is halfway between the two round numbers, and the usual convention in school maths is to round halfway values up. On a number line you can see that numbers above the halfway point are nearer the higher round number.

TRY ITRounding on a number line

Type a number and choose the place to round to. The number line shows the two “round” numbers on either side, the halfway point, and which one is nearer. Use the step buttons to see exactly where the answer changes.

Number: Round to the:

(steps move the number by one tenth of the rounding place)

Worked examples

Example 1: One number, three different roundings

Question: Round 3,746 to the nearest 10, the nearest 100 and the nearest 1,000.

Nearest 10: the tens digit is 4 and the decider (ones) is 6. 6 ≥ 5, so round up: 4 tens become 5 tens → 3,750.
Nearest 100: the hundreds digit is 7 and the decider (tens) is 4. 4 < 5, so round down → 3,700.
Nearest 1,000: the thousands digit is 3 and the decider (hundreds) is 7. Round up → 4,000.

Answer: 3,750; 3,700; 4,000. Notice that the answer depends on which place you round to.

Example 2: A decider of exactly 5

Question: Round 48,650 to the nearest 100 and to the nearest 1,000.

Nearest 100: hundreds digit 6, decider (tens) 5. 5 means round up: 6 hundreds → 7 hundreds → 48,700.
Nearest 1,000: thousands digit 8, decider (hundreds) 6. Round up: 8 thousands → 9 thousands → 49,000.

Answer: 48,700 and 49,000.

Example 3: Rounding large numbers

Question: Round 2,495,318 to the nearest 10,000 and to the nearest million.

Nearest 10,000: the ten-thousands digit is 9 and the decider (thousands) is 5, so round up. 9 ten-thousands + 1 = 10 ten-thousands, so carry 1 into the hundred-thousands place: 249 ten-thousands become 250 ten-thousands → 2,500,000.
Nearest million: the millions digit is 2 and the decider (hundred thousands) is 4. Round down → 2,000,000.

Answer: 2,500,000 and 2,000,000.

Example 4: Rounding up past a 9

Question: Round 69,960 to the nearest 100.

The hundreds digit is 9 and the decider (tens) is 6, so round up.
699 hundreds + 1 = 700 hundreds. Write 700 hundreds as 70,000.

Answer: 70,000. (It is not 69,1000 or 691,000!)

Estimating quantities with a benchmark of 100

How many people are in a big crowd? How many beans are in a jar? Counting every single one would take far too long, so we estimate using a benchmark – a group whose size we know. A benchmark of 100 works well:

Count out 100 objects (or 100 people in one part of a photo) and notice how much space they take up.
Mentally group the rest of the objects into chunks of about the same size.
Count the chunks and multiply by 100.
Verify: if you can, count the real total and see how close you were.

Example 5: Estimating a crowd

Question: A photo of a crowd is divided into equal sections. One section contains about 100 people, and the crowd fills about 12 sections. Estimate the size of the crowd.

Benchmark: 1 section ≈ 100 people.
12 sections ≈ 12 × 100.

Answer: about 1,200 people.

Estimating answers and giving answers to a degree of accuracy

Before you calculate, round each number to make a quick estimate. If your exact answer is far from the estimate, check your working. For example, 412 × 29 ≈ 400 × 30 = 12,000. The exact answer is 11,948, which is close, so it is reasonable.

Sometimes a question asks you to give your answer “to the nearest thousand” or “correct to the nearest hundred dollars”. Work out the exact answer first, then round it once at the end. Example: a school fair raised $18,653. To the nearest hundred dollars this is $18,700 (the tens digit, 5, means round up).

Common mistakes

Rounding in a chain. To round 1,448 to the nearest 100, look only at the tens digit (4) → 1,400. Do not round to 1,450 first and then to 1,500.
Forgetting the zeros. 3,746 to the nearest 100 is 3,700, not 37.
Looking at the wrong digit. The decider is always the digit immediately to the right of the rounding place.
Changing digits on the left. When you round down, the digits to the left of the rounding place stay exactly the same.

Practice questions

Try these yourself first, then open each answer to check your working.

1. Round 8,362 to the nearest 10, the nearest 100 and the nearest 1,000.

Show answer

8,360 (decider 2); 8,400 (decider 6); 8,000 (decider 3).

2. Round 547,500 to the nearest 1,000.

Show answer

548,000. The decider (hundreds digit) is 5, so round up.

3. Round 13,952 to the nearest 100.

Show answer

14,000. The hundreds digit 9 rounds up to 10, so carry: 139 hundreds + 1 = 140 hundreds.

4. Round 7,649,999 to the nearest million and to the nearest 100,000.

Show answer

Nearest million: 8,000,000 (decider 6). Nearest 100,000: 7,600,000 (decider 4).

5. A whole number rounded to the nearest 10 is 250. What are the smallest and largest numbers it could be?

Show answer

Smallest 245, largest 254. (245 rounds up to 250; 255 would round up to 260.)

6. Estimate 4,812 + 3,197 by rounding each number to the nearest 1,000. Then find the exact answer.

Show answer

Estimate: 5,000 + 3,000 = 8,000. Exact: 8,009. Very close.

7. Estimate 58 × 21 by rounding each number to the nearest 10. Then find the exact answer.

Show answer

Estimate: 60 × 20 = 1,200. Exact: 1,218.

8. A photo of a beach is split into 20 equal squares. One square has about 100 people in it. Estimate the number of people on the beach.

Show answer

20 × 100 = about 2,000 people.

9. A builder needs 2,350 bricks. Write this number to the nearest hundred.

Show answer

2,400 (the decider, 5, rounds up).

Quick check

1. When rounding to the nearest 1,000, which digit decides whether you round up or down?

Show answer

The hundreds digit (the digit just to the right of the thousands place).

2. Does 45 round to 40 or 50 (nearest 10)?

Show answer

50. A decider of 5 always rounds up.

3. Why do we estimate before calculating?

Show answer

To get a rough idea of the answer, so we can tell if our exact answer is sensible.

4. What is a benchmark when estimating a quantity?

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A group of known size (such as 100 objects) used to judge how many there are altogether.

Next: Odd, Even, Prime, Composite, Square, Triangular and Rectangular Numbers

Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 1, Term 1, Strand 1.1 Number Operations and Number Theory, Topic 1.1.1 Whole Numbers – Learning Outcomes 1.1.1.4 (rounding to the nearest ten, hundred, thousand and up to millions), 1.1.1.5 (estimating a quantity using 100 as a benchmark and checking by counting) and 1.1.1.8 (solving whole-number problems and giving answers to a stated degree of accuracy).