Discover Mathematics P5: Term 1, Unit 1, Lessons 6–9
GoalRound a decimal to the nearest whole number, tenth, hundredth or thousandth.
New words
round · to replace a number by a nearby one that is easier to usenearest tenth · the closest number with just one digit after the point≈ · a sign that means “is about equal to”
Explanation
To round a decimal, first find the place you are rounding to. Then look only at the digit just to its right. If that digit is 5 or more, the digit in the place you keep goes up by one. If it is 4 or less, the digit stays the same. Every digit after it is dropped. Round 6.748 to the nearest tenth: the tenths digit is 7, the digit to its right is 4, so it stays: 6.7. Round it to the nearest hundredth: the digit to the right of the 4 is 8, so the 4 goes up: 6.75. A number halfway between two neighbours, such as 6.75 to the nearest tenth, rounds up to 6.8.
Round to
Digit to check
Decision
6.748 ≈
whole number
7 (tenths)
7 ≥ 5, up
7
tenth
4 (hundredths)
4 < 5, stay
6.7
hundredth
8 (thousandths)
8 ≥ 5, up
6.75
Worked examples
A rope is 12.35 m long. Round it to the nearest tenth of a metre. The digit to the right of the tenths is 5, so the 3 goes up: 12.4 m. On the number line 12.35 is exactly halfway between 12.3 and 12.4, and by the rule halfway numbers go up.
Round 4.996 to the nearest hundredth. The digit to the right of the hundredths is 6, so the second 9 goes up by one. 9 + 1 = 10, so we write 0 and carry 1, and the carry goes on up the number: 4.996 ≈ 5.00, which is 5. Rounding can change several digits.
★Remember
Look at ONE digit only: the one right next to the place you keep. 5 or more: round up. 4 or less: stay.
Round 18.5 and 0.38 to the nearest whole number. For 18.5 the tenths digit is 5, so 18.5 ≈ 19. For 0.38 the tenths digit is 3, so the whole number stays 0: 0.38 ≈ 0. A small decimal can round to 0.
Class activity
Rounding race. Write ten decimals with three digits after the point on small papers (for example 3.614, 8.095, 12.449). Draw one paper, then roll a die or choose: whole number, tenth or hundredth. The child rounds it and the grown-up checks on a number line drawn on paper. Keep the papers the child rounded correctly.
Practice
1
Round 3.614 to the nearest tenth.
3.6, because the hundredths digit 1 is less than 5.
2
Round 2.095 to the nearest hundredth.
2.10. The thousandths digit is 5, so 9 goes up to 10 and carries: 2.10.
3
Round 26.51 to the nearest whole number.
27, because the tenths digit is 5.
4
Salma rounds 5.47 to the nearest whole number and says 6 because 7 is more than 5. What is her mistake?
She looked at the hundredths digit 7. She must look only at the digit next to the ones place, the tenths digit 4, so 5.47 ≈ 5.
5
Write three different decimals with two places that round to 8.3 when rounded to the nearest tenth.
For example 8.25, 8.30 and 8.34. Any number from 8.25 up to 8.34 works.
