#### Write the decimal expansions of the following numbers which have terminating decimal expansions:

(i) 17/8

(ii) 13/3125

(iii) 7/80

(iv) 6/15

(v) 2²×7/5^{4}

(vi) 237/1500

**Solution:**

**(i) **17/8

17/8 = 2.125

**(ii) **13/3125

13/3125 = 0.00416

**(iii) **7/80

7/80 = 0.0875

**(iv) **6/15

Let us divide both numerator and denominator by 3, we get

6/15 = (6 **÷ **3) / (15 **÷ **3)

= 2/5

Since the denominator is 5,

It is terminating decimal.

6/15 = 0.4

**(v) (**2²×7)/5^{4}

We know that the denominator is 5^{4}

It is a terminating decimal.

**(**2²×7)/5^{4} = (2 × 2 × 7) / (5 × 5 × 5 × 5)

= 28/625

28/625 = 0.0448

It is a terminating decimal.

**(vi) **237/1500

Let us divide both numerator and denominator by 3, we get

237/1500 = (237 **÷ **3) / (1500 **÷ **3)

= 79/500

Since the denominator is 500,

Its factors are, 500 = 2 × 2 × 5 × 5 × 5

= 2^{2} × 5^{3}

It is terminating decimal.

237/1500= 79/500 = 0.1518

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