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What size of numbers does standard 5.NBT.7 refer to? Students are not called to divide a fraction by a fraction until 6th grade, but should they divide a decimal by a decimal? Up to how many digits should the divisor and the dividend be? What is reasonable using strategies based on place value?
7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.The expectations for decimals is limited to thousandths so the largest products would be tenths by hundredths. Then, 5.NBT.6 sets the limits for division: up to four digit dividends and two digit divisors. So, if both the dividend and divisor are decimals, the dividend could be to the hundredths place and four digits, like 34.29 and the divisor could also be to the hundredths place but 2 digits, like .27.
It seems to me that the expectation is for 34.29 / .27 to be handled just like 3429 / 27 with the added step of thinking about the placement of the decimal point. Thinking about the placement of the decimal point is a strategy based on place value. Maybe in this case, you have already established that dividing by .01 results in a dividend that is 100 times larger and since .27 is equivalent to (.01 x 27) we could first divide by .01 getting 3429, and then divide by 27.
Or another alternative might be thinking about how many hundredths make up 34.29. There are 100 one-hundredths in 1 so there are 3400 + 29 hundredths in 34.29. So now we are thinking about how many 27 hundredths are in 3429 hundredths.
From Bill’s reply here:
In the Common Core decimals are treated simply as a different way of writing fractions with denominator 10, 100, and so on.
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