Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
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
Our number system is built on one simple relationship between neighboring places. A digit is worth 10 times as much as the same digit one place to its right, and one tenth of what it would be worth one place to its left. In 4,444, the 4 in the hundreds place is worth 400, ten times the 40 next to it and one tenth of the 4,000 beside it.
In fourth grade students used this idea with whole numbers. In fifth grade it is extended across the decimal point, which is where it really pays off: the 7 in 0.7 is worth 7 tenths, which is ten times the 7 in 0.07. Understanding that the same pattern continues to the right of the ones place explains why decimals work at all, and it is the reason multiplying or dividing by 10 shifts every digit one place. Students should describe these relationships in words and with place value charts, not just recite them.
Some students believe tenths and hundredths follow a different rule. A chart that runs from thousands to thousandths, with the same 'times 10' arrows all the way along, corrects this.
Moving left makes a digit worth more, moving right makes it worth less. Students who mix this up will say the 5 in 0.05 is bigger than the 5 in 0.5.
Hearing 'the next place', students sometimes say a digit is worth 10 more rather than 10 times as much. Comparing 30 and 300 shows the jump is multiplicative.
The place right of the decimal point is tenths, because there is no oneths place. The ones place is the center of the symmetry, not the decimal point itself.
In the number 6.66, how many times greater is the value of the 6 in the ones place than the value of the 6 in the hundredths place?
Answer: The 6 in the ones place is worth 100 times as much as the 6 in the hundredths place.
Base-ten blocks with a redefined whole (a flat as 1, a rod as 0.1, a small cube as 0.01) let students physically see that ten of one piece makes one of the next. Pair this with a place value chart where students draw '× 10' arrows to the left and '× 1/10' arrows to the right.
Assessment items ask how the value of a digit in one position compares with the same digit in another, often with decimals, and sometimes as part of a multiple-select item.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) 10 times
The hundreds place is one place to the left of the tens place, so a digit there is worth 10 times as much: 500 is 10 times 50.
Answer: 0.04
The 4 is in the hundredths place, so it is worth 4 hundredths, which is 0.04.
Answer: D) 10 times
Tenths are one place to the left of hundredths, so 0.7 is 10 times 0.07.
Answer: 100
The hundreds digit is worth 300 and the ones digit is worth 3. 300 ÷ 3 = 100, two places apart means 10 × 10.
Answer: B) The 9 in the tenths place is worth 1/10 of the 9 in the ones place
The ones digit is worth 9 and the tenths digit is worth 0.9, which is one tenth of 9.
Answer: 3
Moving one place to the left multiplies the value by 10: 0.3 × 10 = 3.
A full lesson with slides, activities and an exit ticket on place value: ten times and one tenth, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NBT.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn place value: ten times and one tenth into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Fourth grade (4.NBT.A.1) works with whole numbers and the 'ten times' relationship. Fifth grade adds the 'one tenth' direction and extends both relationships to decimals.
Yes. Fifth grade place value work runs to thousandths, so students should name and compare tenths, hundredths and thousandths.