S1 Maths | Approximation and Estimation: Rounding, Significant Figures, Checking Tutor Prep Guide

2026-11-14

Tutor lesson-prep guides · Secondary Maths

A student calls 0.006254 four significant figures because he starts counting after the decimal point, and another is happy with 48.6 times 3.1 equal to 1506.6. This lesson separates rounding, counting significant figures and estimating first, one rule each.

Objectives — By the end students can: (1) round 3.4782 to two decimal places, giving 3.48, and to one, giving 3.5; (2) state that 0.006254 has two significant figures and that two significant figures give 0.0063, explaining that counting starts at the first non-zero digit; (3) estimate 48.6 times 3.1 as about 150 against a true value of 150.66 and say why 1506.6 cannot be right.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Place value	What place is the 4 in 3.4782?	The tenths place
Rounding decision	If the first digit you drop is 5, do you round up?	Yes, 5 or above rounds up
Mental multiplication	What is 50 times 3?	150

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Start from one real number	Write 3.4782 and ask what it is if only two decimal places are kept	Answer and give a reason
5-14 min	Rounding	Show two decimal places giving 3.48 and one giving 3.5, stress looking only at the first digit dropped	Round 0.006254 to four decimal places
14-24 min	Significant figures	Count from 0.006254: the 6 is first, the 2 is second, so two significant figures give 0.0063	Count the significant figures in three numbers
24-33 min	Estimate first	Turn 48.6 times 3.1 into 50 times 3, which is 150, then compute 150.66 and compare	Say how far the estimate is from the true value
33-41 min	Three independent items	Hand out a rounding, a significant figure and an estimation item, watching for counting from the decimal point	Write which place is being kept first
41-45 min	Exit check	Three oral questions: 3.4782 to two decimals, significant figures in 0.006254, and 19.8 times 5.2	Answer aloud with a reason

03 Teaching script (read it out)

Scene 1: Act 1: rounding looks at one digit only

“For 3.4782 to two decimal places, look at the third decimal, which is 8. Since 8 is 5 or more, the 7 rounds up to 8, so the answer is 3.48. To one decimal place, look at the 7 and round the 4 up to 5, giving 3.5. The rule is one sentence: look only at the first digit you drop, and nothing beyond it counts. That is why you never round digit by digit from the right, which is the most common slip.”

Students repeat: look only at the first digit dropped

Scene 2: Act 2: significant figures start at the first non-zero digit

“In 0.006254 the three zeros in front are not significant, they only place the decimal point. The first non-zero digit is 6 and the second is 2. For two significant figures look at the third digit, which is 5, so round up to 0.0063. The usual error is counting from the decimal point and saying four. Sweep from the left and start at the first digit that is not zero.”

Students repeat: start at the first non-zero digit

Scene 3: Act 3: estimate first and the answer has a defence

“For 48.6 times 3.1, take 48.6 as 50 and 3.1 as 3, so 50 times 3 is 150. The true value is 150.66, less than one per cent away, so the answer stands. If someone gets 1506.6 the answer is ten times too big, which means the decimal point moved. An estimate is not the answer, it is the check, so do it in one significant figure after every calculation and most careless errors die before the paper is handed in.”

Students repeat: estimate first, more than ten per cent means redo

04 Question types and worked steps

Type	Example	Steps	Answer
Round to a place	Round 3.4782 to two decimal places	(1) Name the place kept (2) look at the next digit (3) round up at 5 or more (4) delete the rest	3.48
Count significant figures	How many significant figures in 0.006254?	(1) Skip leading zeros (2) start at the first non-zero digit (3) count to the last digit (4) state the count	Two, the 6 and the 2
Keep a set number of significant figures	Keep two significant figures in 0.006254	(1) Find the first non-zero digit (2) count to the second (3) look at the next digit (4) keep the original place value	0.0063
Estimate and check	Estimate 48.6 times 3.1 and judge 1506.6	(1) One significant figure each (2) multiply mentally (3) compare with the true value (4) redo if more than ten per cent out	About 150, true value 150.66

Sanity check (teach this): Checks that must hold: rounding never changes the size of the number, so 3.4782 to two decimals stays near 3, and 34.8 means a place value slip; significant figures can never outnumber the actual digits, so 0.006254 has at most four; an estimate should land within about ten per cent, and 150 against 150.66 is under one per cent while 1506.6 is ten times out, which is a decimal point error; 19.8 times 5.2 estimated at 100 against 102.96 is three per cent out and acceptable; 398 times 21 estimated at 8000 against 8358 is 4.5 per cent out; 1298 divided by 4.1 estimated at 325 against 316.6 is 2.6 per cent out.

05 Independent practice (3 questions)

Question	Answer	What to watch
Keep two significant figures in 0.006254.	0.0063, because the third digit is 5 and rounds up	0.0062 means the next digit was misread
Estimate 19.8 times 5.2 and say how far the true value lies.	20 times 5 is 100, and the true value 102.96 is about three per cent away	1000 means the decimal point moved
Roughly what is 1298 divided by 4.1?	1300 divided by 4 is 325, and the true value is about 316.6	31.6 means one place was lost

06 Common mistakes and what to say

Mistake	Student writes	Say this
Counting significant figures from the decimal point	“0.006254 has four significant figures.”	“Significant figures start at the first non-zero digit: the 6 is first and the 2 is second, so there are only two.”
Rounding digit by digit from the right	“3.4782 to one decimal place means 8 rounds up, so it becomes 3.5 and then…”	“Look only at the first digit dropped. To one decimal place look at the 7, so the answer is 3.5, and the 82 plays no part.”
Writing the estimate as the answer	“48.6 times 3.1 equals 150.”	“The estimate is the check. The answer is the true value, 150.66.”
Not questioning an impossible answer	“48.6 times 3.1 equals 1506.6.”	“50 times 3 is about 150, so your answer is ten times too big, which means the decimal point is wrong. Redo it.”

07 Homework (paper, section and question numbers)

Redo Act 1: round 3.4782 to two and to one decimal place, and write which digit you looked at — Chapter practice, question 1
Do two significant figure items: 0.006254 and 45600 to two significant figures each — Chapter practice, question 2
Preview: estimate 398 times 21, then write the estimate, the true value and the percentage error — Chapter practice, question 3

08 Exit check (last 5 minutes)

Question	Answer	Decision
What is 3.4782 to two decimal places?	3.48, because the third digit is 8 and rounds up	An answer of 3.47 means the wrong digit was read
How many significant figures does 0.006254 have?	Two, the 6 and the 2	An answer of four means counting from the decimal point
Roughly what is 19.8 times 5.2?	About 100, with a true value of 102.96	An answer of 1000 means place value is unclear

09 Tutor FAQ

Why teach estimation when the exact value is available?

Because an estimate catches decimal point and place value errors in seconds, while an exact calculation never tells you the answer is impossible. That self-check matters most in an exam.

Why do leading zeros not count as significant figures?

They only mark where the decimal point sits and vanish in scientific notation: 0.006254 becomes 6.254 times ten to the minus three. Only 6, 2, 5 and 4 carry information.

My student keeps losing a place while rounding. What fixes it?

Have them write which place they are keeping before touching the digits, and underline that column. If the place is written down, it cannot be counted wrongly.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.