Final answer:
To convert a decimal to a fraction, you write the digits to the right of the decimal point over the place value of the last digit, and this is true. Zeros may be used as placeholders when moving the decimal point. Understanding place value is crucial in performing conversions and trailing zeros in decimals are significant.
Step-by-step explanation:
The statement that to change a decimal to a fraction, we write the digits to the right of the decimal point over the place value of the last digit in the number is true. For instance, if we have the decimal 0.75, we notice that the last digit '5' is in the hundredths place. Therefore, we can write this as a fraction with the numerator being 75 (the digits to the right of the decimal) and the denominator being 100 (the place value of the last digit). The fraction is ⅓75/100, which can be simplified to 3/4.
Sometimes, when converting a number and we need to move the decimal point, there may not be enough decimal places. In this scenario, we add zeros as placeholders. For example, the multiplication of 2.4 by 100 moves the decimal two places to the right, resulting in the number 240. The zero acts as a placeholder in the hundredths place.
Understanding the place value of digits in a decimal number is essential. In 231.45, for instance, each digit has a specific place value relative to the decimal point: 2 is in the hundreds place, 3 in the tens, 1 in the ones, 4 in the tenths, and 5 in the hundredths place.
When performing conversions, it is important to note that trailing zeros in a number with a decimal point are significant, whether they occur before or after the decimal point.