Fractions and Decimals - Division of Decimal Numbers

Division by Powers of 10: When dividing a decimal number by $10$, $100$, or $1000$, the decimal point shifts to the left by as many places as there are zeros in the divisor. For example, in $31.5 \div 100$, the decimal point 'jumps' two places to the left, resulting in $0.315$.

Division of a Decimal by a Whole Number: Perform the division just like whole numbers, ignoring the decimal point initially. Once the division is done, place the decimal point in the quotient directly above its position in the dividend. Imagine a vertical dotted line extending from the dividend's decimal up into the quotient to ensure perfect alignment.

Division of a Decimal by another Decimal: To solve this, convert the divisor into a whole number by shifting its decimal point to the right until it reaches the end. You must then shift the decimal point in the dividend to the right by the same number of places. This is visually equivalent to multiplying both numbers by a power of $10$ to maintain the ratio.

Handling Zeros in the Dividend: If the divisor does not go into the dividend evenly, you can append zeros to the right of the decimal point in the dividend (as $5.2$ is the same as $5.200$) and continue dividing until the remainder is zero or the decimals start repeating.

Placement of Zero in Quotient: When the divisor is larger than the part of the dividend being divided, we place a $0$ in the quotient. This is common when the whole number part of a decimal is smaller than the divisor, such as in $0.24 \div 6$, where the quotient starts with $0$.

Estimation for Accuracy: Before calculating, round the decimal to the nearest whole number to estimate the answer. For $49.6 \div 10.2$, think of it as $50 \div 10$, so your final answer should be close to $5$. This acts as a visual check to ensure the decimal point is in the correct place.