Writing decimal numbers
Writing decimal numbers from words uses the word 'and' to place the decimal point, and the last place-value word (thousandths, hundredths, tenths) determines how many decimal places to include. 'Three and forty-five thousandths' = 3.045 — the number 45 must fill the thousandths position, requiring a leading zero in the hundredths place. This Grade 7 math skill from Saxon Math, Course 2 reinforces place value understanding for decimals and is essential for dictation in math class, reading word problems, and converting between verbal and numeric representations of precise measurements.
Key Concepts
Property To write a decimal number from words, use 'and' to place the decimal point. The last word (e.g., 'thousandths') tells you the total number of decimal places. Fill the places with the number, using leading zeros as placeholders if needed.
Examples 'Eighty two thousandths' is written as $0.082$, with a zero to hold the tenths place. 'Three hundred and six hundredths' is written as $300.06$. 'Fourteen and five tenths' is written as $14.5$.
Explanation Writing decimals is like solving a puzzle. The word 'and' tells you exactly where to put the decimal point. The last word, like 'thousandths,' tells you how many slots you need to fill after the dot (three for thousandths!). Then, you just drop the number in, making sure the last digit lands in the final slot. Add zeros if you have empty spaces!
Common Questions
How do I write a decimal number from words?
Use 'and' to place the decimal point. The last word tells you the final place value — count that many decimal places and write the given number to fill them, using leading zeros if needed.
How do I write 'three and forty-five thousandths' as a number?
The 'and' places the decimal: 3. Then 'forty-five thousandths' means 45 in the thousandths position. Since thousandths is 3 decimal places, write 3.045 (zero in hundredths, 45 in tenths-hundredths-thousandths is wrong — count from the decimal: 0.045).
What do 'tenths', 'hundredths', and 'thousandths' mean?
These are place values to the right of the decimal point: tenths is 1 decimal place (0.1), hundredths is 2 places (0.01), thousandths is 3 places (0.001).
What if the decimal number requires leading zeros?
If the number does not fill all required decimal places, insert zeros as placeholders. 'Seven hundredths' = 0.07, not 0.7 — the 7 must be in the hundredths (second) position.
When do students learn to write decimal numbers from words?
Reading and writing decimals from words is introduced in Grade 4-5 and reinforced in Grade 7. Saxon Math, Course 2 covers it in Chapter 8.
Why is 'and' reserved for the decimal point?
In formal mathematical notation, 'and' signals the decimal point. Using 'and' in whole number names (like 'two hundred and fifty') creates ambiguity that could imply a decimal.
How does writing decimal numbers from words connect to place value?
The connection is direct — the final place-value word dictates where the last digit lands, requiring you to fill all intermediate places, using zeros as needed for accuracy.