If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?

Concept

When both the dividend and the divisor of a division are scaled by powers of 10, the quotient scales by the ratio of those two scale factors: dividing the dividend by 10^a and the divisor by 10^b changes the quotient to (original quotient) ÷ 10^(a−b).

Application

1. Given: 2994 ÷ 14.5 = 172.

2. Multiply numerator and denominator of 29.94 ÷ 1.45 by 100 to clear the decimals: 29.94 × 100 = 2994 and 1.45 × 100 = 145, so 29.94 ÷ 1.45 = 2994 ÷ 145.

3. Relate 145 to the given divisor: 145 = 14.5 × 10.

4. Substitute: 2994 ÷ 145 = 2994 ÷ (14.5 × 10) = (2994 ÷ 14.5) ÷ 10.

5. Use the given value: (2994 ÷ 14.5) ÷ 10 = 172 ÷ 10 = 17.2.

Cross-check

Track the decimal shifts directly: going from 2994 to 29.94 divides the dividend by 100, while going from 14.5 to 1.45 divides the divisor by only 10. The net effect on the quotient is a division by 100 combined with a further multiplication by 10 (from the smaller divisor shift), i.e. an overall division by 10 — confirming 172 ÷ 10 = 17.2.