☰ Year plan · Mathematics

Reading, comparing and writing decimals

Week 1 · Reading, comparing and writing decimals to thousandths · 3 lessons
2

Moving a digit left or right

Discover Mathematics P5: Term 1, Unit 1, Lessons 1–5
GoalSee that moving a digit one place left makes it ten times bigger and one place right makes it ten times smaller.
New words
place · the position of a digit in a number, such as tens or tenthstimes as much · ten times as much means multiplied by 10place holder · a zero that keeps the other digits in their right places
Explanation

A digit changes its value when it changes its place. Look at the digit 4 in 0.004: it is 4 thousandths. Move it one place left and it is 0.04, another place and it is 0.4, then 4, then 40. Each step to the left multiplies the value by 10. Going back to the right divides by 10 each time. The same happens to every digit of a number when we multiply it: 3.5 × 10 moves every digit one place left and gives 35. Multiplying by 100 moves every digit two places left: 350, and a zero holds the empty ones place. Dividing moves digits to the right: 3.5 ÷ 10 = 0.35. The decimal point stays where it is; it is the digits that move.

NumberTensOnesTenthsHundredthsThousandths
404
44
0.44
0.044
0.0044
Worked examples
NumberTensOnesTenths
2.626
2626
Seif has 2.6 kg of dates. A shop sells 10 times as much. 2.6 × 10 = 26, so the shop sells 26 kg. Every digit moved one place left: the 2 went from the ones place to the tens place (2 to 20), and the 6 went from the tenths place to the ones place (0.6 to 6).
NumberOnesTenthsHundredthsThousandths
4.75475
0.4750475
A bag holds 4.75 kg of rice and is shared equally into 10 small packs. 4.75 ÷ 10 = 0.475, so each pack holds 0.475 kg. Every digit moved one place right: the 4 went from the ones place to the tenths place, the 7 to the hundredths place and the 5 to the thousandths place.
★Remember
× 10, × 100: the digits move left, one place for every zero. ÷ 10, ÷ 100: the digits move right.
Fill the gaps: 0.063 × 100 = 6.3, because the digits move two places left. And 6.3 ÷ 100 = 0.063, because they move two places back. Multiplying and dividing by the same number undo each other.
Class activity

Slide the digits. Write the digits 3, 8 and 5 on three small papers and put them in a row with a coin as the decimal point after the first paper: 3.85. Multiply by 10 by sliding each paper one place left (put a paper marked 0 to fill gaps), and divide by 10 by sliding them right. Write each result and say how many times bigger or smaller it is than 3.85.

Practice
1
Work out 5.8 × 10, 5.8 × 100 and 5.8 ÷ 10.
2
The digit 7 in 0.27 moves two places left (the number is multiplied by 100). Where does it stand now and what is it worth?
3
A number divided by 10 gives 0.46. What was the number?
4
Hana says 3.4 × 10 = 3.40. Is she right? Explain.
5
Compare the digit 3 in 30.2 with the digit 3 in 0.32. How many times greater is the first one?