Read, write, and compare decimals to thousandths.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Decimals to thousandths can be written in three ways, and fifth graders should move fluently between them. The numeral 347.392 can be read as 'three hundred forty-seven and three hundred ninety-two thousandths', and written in expanded form as 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). The word 'and' marks the decimal point, and the last place named (thousandths) tells the unit of the decimal part.
Comparing decimals depends on place value, not on how many digits a number has. To compare 0.45 and 0.405, students line the digits up by place and look from the left: both have 4 tenths, but 0.45 has 5 hundredths while 0.405 has 0 hundredths, so 0.45 > 0.405. Writing 0.45 as 0.450 can help, since both numbers are then counted in thousandths. Students record each comparison with >, = or < and should be able to justify it by naming the place where the numbers first differ.
Students who think 0.125 > 0.3 because 125 is more than 3 are comparing digit strings, not values. 0.3 is 3 tenths, which is 300 thousandths, so it is larger.
The opposite error also appears: thinking 0.4 > 0.45 because tenths are 'bigger pieces'. Rewriting both in hundredths (40 and 45) settles it.
'Six and fourteen thousandths' is often written 6.14. Fourteen thousandths needs three decimal places, so it is 6.014.
Reading 305 as 'three hundred and five' blurs where the decimal point is. In decimal reading, 'and' should be kept only for the decimal point.
Which is greater, 2.508 or 2.58? Write the comparison with a symbol and give 2.508 in expanded form.
Answer: 2.508 < 2.58, and 2.508 = 2 × 1 + 5 × (1/10) + 0 × (1/100) + 8 × (1/1000).
Place value charts with columns from hundreds to thousandths help students line up digits correctly. Decimal grids (a 10 by 10 square for hundredths) give a visual check of size, and money and metric measurements offer familiar contexts for tenths and hundredths.
Typical items ask students to choose the numeral that matches a word form, pick the correct expanded form, or complete a comparison with a symbol. Ordering four or five decimals with different numbers of digits is a frequent multi-select task.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 4.036
Thirty-six thousandths needs three decimal places: 0.036. Adding the 4 ones gives 4.036.
Answer: A) >
0.7 = 0.70, which is 70 hundredths. 0.69 is 69 hundredths, so 0.7 > 0.69.
Answer: B) 0.209, 0.25, 0.3
In thousandths the numbers are 209, 250 and 300, so the order is 0.209, 0.25, 0.3.
Answer: 62.407
There are 6 tens, 2 ones, 4 tenths, 0 hundredths and 7 thousandths, so the number is 62.407. The 0 holds the hundredths place.
Answer: D) Fifteen and six hundredths
The 6 is in the hundredths place, so 15.06 is read 'fifteen and six hundredths'.
Answer: A) 0.1
0.1 has 1 tenth, while every other option has 0 tenths. So 0.1 is the greatest.
A full lesson with slides, activities and an exit ticket on reading, writing and comparing decimals, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NBT.A.3 with an answer key, ready in about a minute.
Make a worksheet →Turn reading, writing and comparing decimals into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Writing each place as a digit times a fraction such as 1/100 connects decimals to the fraction work in 4.NF.C.6 and shows what each digit is really worth.
Yes. Writing 0.4 as 0.400 does not change its value and lets students compare both numbers in thousandths, as long as they understand why the zeros are allowed.