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:

1. Count along from the first non-zero digit to the last significant figure you want to keep.
2. 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.
3. 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.

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?

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

1. (a) The first figure is 1 (millions). The next digit is 8, so round up to 2,000,000.
2. (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.

1. The first non-zero digit is 5. Keep 5 and 0.
2. 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.

1. Keep 6, 9, 9. The next digit is 6, so the last 9 rounds up.
2. 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.

1. (a) 387 ≈ 400 and 52 ≈ 50, so 400 × 50 = 20,000.
2. (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?

1. Round each price to 1 s.f.: $40, $20 and $8.
2. 40 + 20 + 8 = 68.
3. 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.

1. (a) 200 + 375 − 2 = 573.
2. (b) Halve and double: 70 × 6 = 420.
3. (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.

Quick check

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.

© 2026 Vedesh Kungebeharry. All rights reserved.