1. The following equations involve different quantities and use different operations, yet produce the same result. Use a place value chart and words to explain why this is true.
4.13 × 103 = 4130 413,000 ÷ 102 = 4130
2. Use an area model to explain the product of 4.6 and 3. Write the product in standard form, word form, and expanded form.
3. Compare using >, <, or =.
a. 2 tenths + 11 hundredths ______ 0.13
b. 13 tenths + 8 tenths + 32 hundredths ______ 2.42
c. 342 hundredths + 7 tenths ______ 3 + 49 hundredths
d. 2 + 31 × 1/10 + 14 × 1/100 ______ 2.324
e. 14 + 72 × 1/10 + 4 × 1/1000 ______ 21.24
f. 0.3 × 102 + 0.007 × 103 ______ 0.3 × 10 + 0.7 × 102
3. Compare using >, <, or =.
a. 2 tenths + 11 hundredths ______ 0.13
b. 13 tenths + 8 tenths + 32 hundredths ______ 2.42
c. 342 hundredths + 7 tenths ______ 3 + 49 hundredths
d. 2 + 31 × 1/10 + 14 × 1/100 ______ 2.324
e. 14 + 72 × 1/10 + 4 × 1/1000 ______ 21.24
f. 0.3 × 102 + 0.007 × 103 ______ 0.3 × 10 + 0.7 × 102
3. Compare using >, <, or =.
a. 2 tenths + 11 hundredths ______ 0.13
b. 13 tenths + 8 tenths + 32 hundredths ______ 2.42
c. 342 hundredths + 7 tenths ______ 3 + 49 hundredths
d. 2 + 31 × 1/10 + 14 × 1/100 ______ 2.324
e. 14 + 72 × 1/10 + 4 × 1/1000 ______ 21.24
f. 0.3 × 102 + 0.007 × 103 ______ 0.3 × 10 + 0.7 × 102
4a.
Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine. a. About how much medicine did he make in grams? Estimate the amount of each chemical by rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.
4b. Find the actual amount of medicine mixed by Dr. Mann. What is the difference between your estimate and the actual amount?
4c. How many grams are in one dose of medicine? Explain your strategy for solving this problem
4d. Round the weight of one dose to the nearest gram.