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Hello,
A question regarding the standard:
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.Please clarify if the bolded part of this standard is inclusive of terminating decimals, previously defined as: A decimal is called terminating if its repeating digit is 0.
Do the 7th grade standards (7.NS.2d or any other 6-8 standard) require converting terminating decimals into a rational number?
Thank you!
I think the standard is focused on decimal expansions which repeat in digits other than zero, but those are certainly included here. The statement “understand informally that every number has a decimal expansion” seems to me to include rationals with a repeating digit of zero.
That being said, grade 4 is the place where we start to see terminating decimals rewritten as rational numbers. 4.NF.6 asks students to “use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100.” Then in grade 5, decimals and decimal fractions are extended to the thousandths. (5.NBT.3) Also in grade 5, in 5.NBT.1, the ground work is laid for generalizing terminating decimals to any place – “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.”
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