Discover Mathematics P4: Term 2, Unit 10, Lessons 5–8
GoalRead a decimal as a fraction with denominator 10 or 100, and write such a fraction as a decimal.
New words
decimal · a number written with a decimal point, such as 0.7 or 2.35denominator · the number below the line of a fraction; it tells how many equal parts the whole is cut intomixed number · a whole number and a fraction together, such as 3 6/10
Explanation
A decimal can be read as a fraction. First count the digits after the decimal point. One digit means tenths, so the denominator is 10. Two digits mean hundredths, so the denominator is 100. The digits after the point, read as one number, are the numerator. So 0.7 = 7/10, 0.43 = 43/100 and 0.07 = 7/100 (the zero in front of the 7 is dropped from the numerator but it told us we have hundredths). When the decimal has a whole part, keep it: 2.35 = 2 35/100, a mixed number. To go the other way, look at the denominator. 9/10 = 0.9 has one digit after the point. 29/100 = 0.29 has two. For 5/100 we need two digits, so we write a zero in the tenths place: 0.05.
0.7
0.07
0.43
Digits after the point
1
2
2
Denominator
10
100
100
Fraction
7/10
7/100
43/100
Worked examples
Read 0.58 as a fraction. There are two digits after the point, so we have hundredths and the denominator is 100. The digits 58 make the numerator: 0.58 = 58/100, read fifty-eight hundredths. On the grid, 58 of the 100 squares are shaded.
Decimal
3.6
4.09
Mixed number
3 6/10
4 9/100
Write 3.6 as a mixed number and 4 9/100 as a decimal. In 3.6 the whole part is 3 and there is one digit after the point, so 3.6 = 3 6/10. In 4 9/100 the fraction 9/100 has denominator 100, so it needs two places after the point, and the tenths place gets a zero: 4 9/100 = 4.09.
Omar writes 0.5 = 5/100. That is a mistake. There is only one digit after the point, so the denominator is 10: 0.5 = 5/10. The fraction 5/100 is the decimal 0.05. In the picture the first bar shows 5/10 and the second shows 5/100, which is much smaller.
Class activity
Decimal cards. On eight small papers write four decimals (0.3, 0.09, 0.45 and 2.7) and, on the other four papers, their fractions (3/10, 9/100, 45/100 and 2 7/10). Mix the papers face down. Take turns to turn over two papers; if they name the same number, keep the pair and say it aloud.
Practice
1
Write 0.81 as a fraction.
81/100.
2
Write 0.6 as a fraction with denominator 10.
6/10.
3
Write 7/100 as a decimal.
0.07 (a zero holds the tenths place).
4
Write 5 3/10 as a decimal.
5.3.
5
Nour writes 0.04 = 4/10. Is she right?
No. There are two digits after the point, so the denominator is 100: 0.04 = 4/100.
