Multiply or divide as indicated.19.967÷9.74

Verified step by step guidance

1. Identify the operation: The problem requires division of two decimal numbers, specifically dividing 19.967 by 9.74.
2. Rewrite the division as a fraction: \(\frac{19.967}{9.74}\).
3. To simplify the division of decimals, multiply both the numerator and the denominator by a power of 10 that will make the denominator a whole number. Since 9.74 has two decimal places, multiply numerator and denominator by 100:
4. \(\frac{19.967 \times 100}{9.74 \times 100} = \frac{1996.7}{974}\).
5. Now, perform the division of the two whole numbers (or decimals with fewer decimal places) to find the quotient.

Key Concepts

Division of Decimal Numbers

Dividing decimal numbers involves determining how many times the divisor fits into the dividend. It requires aligning the decimal points properly and sometimes converting the divisor into a whole number by multiplying both numbers by a power of 10.

Decimal Point Placement

When dividing decimals, the decimal point in the quotient is placed directly above its position in the dividend after adjusting the divisor to a whole number. Correct placement ensures the accuracy of the result.

Simplifying the Division

To simplify division with decimals, multiply both the dividend and divisor by the same power of 10 to eliminate decimals in the divisor. This transforms the problem into dividing whole numbers, making calculations easier.