In this Grade 5 lesson from enVision Mathematics Chapter 1, students learn to read and write decimals to the thousandths place by connecting fractions with denominators of 1,000 to their decimal equivalents using place-value charts. Students practice converting between forms such as 4/1,000 and 0.004, and explore how the value of a digit changes by a factor of 10 across the tenths, hundredths, and thousandths places.
Section 1
Writing Fractions as Thousandths Decimals
A fraction with a denominator of is equivalent to a decimal that extends to the thousandths place, which is the third position to the right of the decimal point.
Section 2
Converting Fractions to Decimals
To convert a fraction with a denominator of 10, 100, or 1,000 to a decimal, write the numerator so its last digit is in the place value indicated by the denominator. The tenths place is one position after the decimal, hundredths is two, and thousandths is three.
Section 3
Converting Terminating Decimals to Fractions
To convert a terminating decimal to a fraction, write the digits of the decimal in the numerator. The denominator is a power of 10 with the same number of zeros as there are decimal places. Then, simplify the fraction to its lowest terms.
To change a decimal into a fraction, use its place value to determine the denominator. The number of digits after the decimal point tells you the number of zeros in the denominator (e.g., two places means a denominator of 100). The digits themselves form the numerator. Always remember to simplify the resulting fraction.
Section 4
Decimal Place Value Relationships
The value of a digit in a decimal number is times the value of the digit to its right and the value of the digit to its left.
Our number system is based on powers of ten. As you move from left to right on the place value chart, the value of each position is one-tenth of the value of the position to its left. This means a digit in one place is ten times as great as the same digit in the place to its right. This relationship holds true for both whole numbers and decimals.
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Section 1
Writing Fractions as Thousandths Decimals
A fraction with a denominator of is equivalent to a decimal that extends to the thousandths place, which is the third position to the right of the decimal point.
Section 2
Converting Fractions to Decimals
To convert a fraction with a denominator of 10, 100, or 1,000 to a decimal, write the numerator so its last digit is in the place value indicated by the denominator. The tenths place is one position after the decimal, hundredths is two, and thousandths is three.
Section 3
Converting Terminating Decimals to Fractions
To convert a terminating decimal to a fraction, write the digits of the decimal in the numerator. The denominator is a power of 10 with the same number of zeros as there are decimal places. Then, simplify the fraction to its lowest terms.
To change a decimal into a fraction, use its place value to determine the denominator. The number of digits after the decimal point tells you the number of zeros in the denominator (e.g., two places means a denominator of 100). The digits themselves form the numerator. Always remember to simplify the resulting fraction.
Section 4
Decimal Place Value Relationships
The value of a digit in a decimal number is times the value of the digit to its right and the value of the digit to its left.
Our number system is based on powers of ten. As you move from left to right on the place value chart, the value of each position is one-tenth of the value of the position to its left. This means a digit in one place is ten times as great as the same digit in the place to its right. This relationship holds true for both whole numbers and decimals.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter