For the lengths shown below write the measurements and read out the measures in words.

Question

Homi · Accepted Answer

We need to read the lengths shown on the rulers and write them in numbers and words. Each small mark on the ruler represents one-hundredth of a unit.

Step 1 — Understanding the ruler scale

Let us look at the ruler markings. The large numbers like 5 and 15 are whole units. Between each whole unit, there are 10 longer marks. Each of these marks represents one-tenth of a unit. For example, after 5, we see $5 \frac{1}{10}$ , $5 \frac{2}{10}$ , and so on. Between each tenth mark, there are 10 smaller marks. Each of these small marks represents one-tenth of a tenth. One-tenth of a tenth is one-hundredth. So, each small mark is $\frac{1}{100}$ of a unit.

Step 2 — Measuring the first length

Let us find the length of the first object on the top ruler. The object ends after the 5 mark. It goes past $5 \frac{3}{10}$ . We count the small marks after $5 \frac{3}{10}$ . There are 7 small marks. Each small mark is $\frac{1}{100}$ . So, this is $\frac{7}{100}$ . The total length is 5 whole units, plus 3 tenths, plus 7 hundredths.

$5 + \frac{3}{10} + \frac{7}{100}$

To add these, we change $\frac{3}{10}$ to hundredths. $\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}$ .

$5 + \frac{30}{100} + \frac{7}{100}$

$= 5 \frac{37}{100}$

We can also write this as an improper fraction. $= \frac{5 \times 100 + 37}{100}$

$\boxed{\frac{537}{100}}$

In words, this length is Five and three-tenths and seven-hundredths. It is also Five and thirty-seven-hundredths. It is also Five hundred thirty-seven-hundredths.

Diagram 1

Step 3 — Measuring the second length

Let us find the length of the second object on the bottom ruler. The object ends after the 15 mark. It goes past 15 whole units. We count the small marks after 15. There are 3 small marks. Each small mark is $\frac{1}{100}$ . So, this is $\frac{3}{100}$ . The total length is 15 whole units, plus 3 hundredths.

$15 + \frac{3}{100}$

$= 15 \frac{3}{100}$

We can also write this as an improper fraction. $= \frac{15 \times 100 + 3}{100}$

$\boxed{\frac{1503}{100}}$

In words, this length is Fifteen and three-hundredths. It is also One thousand five hundred three-hundredths.

Step 4 — Writing the third measurement

Let us consider the measurement $7 \frac{5}{10} \frac{2}{100}$ . This means 7 whole units, 5 tenths, and 2 hundredths. We combine the tenths and hundredths. $\frac{5}{10} = \frac{50}{100}$ .

$7 + \frac{50}{100} + \frac{2}{100}$

$= 7 \frac{52}{100}$

We can also write this as an improper fraction. $= \frac{7 \times 100 + 52}{100}$

$\boxed{\frac{752}{100}}$

In words, this length is Seven and five-tenths and two-hundredths. It is also Seven and fifty-two-hundredths. It is also Seven hundred fifty-two-hundredths.

Step 5 — Writing the fourth measurement

Let us consider the measurement $9 \frac{8}{10}$ . This means 9 whole units and 8 tenths. We can write 8 tenths as hundredths. $\frac{8}{10} = \frac{8 \times 10}{10 \times 10} = \frac{80}{100}$ .

$9 + \frac{80}{100}$

$= 9 \frac{80}{100}$

We can also write this as an improper fraction. $= \frac{9 \times 100 + 80}{100}$

$\boxed{\frac{980}{100}}$

In words, this length is Nine and eight-tenths. It is also Nine and eighty-hundredths. It is also Nine hundred eighty-hundredths.

Answer

(i) $5 \frac{3}{10} \frac{7}{100}$ : Five and three-tenths and seven-hundredths, or $5 \frac{37}{100}$ (Five and thirty-seven-hundredths), or $537/100$ (Five hundred thirty-seven-hundredths) (ii) $15 \frac{3}{100}$ : Fifteen and three-hundredths, or $1503/100$ (One thousand five hundred three-hundredths) (iii) $7 \frac{5}{10} \frac{2}{100}$ : Seven and five-tenths and two-hundredths, or $7 \frac{52}{100}$ (Seven and fifty-two-hundredths), or $752/100$ (Seven hundred fifty-two-hundredths) (iv) $9 \frac{8}{10}$ : Nine and eight-tenths, or $9 \frac{80}{100}$ (Nine and eighty-hundredths), or $980/100$ (Nine hundred eighty-hundredths)

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