Math

QuestionCalculate and round the following with proper significant figures and units:
a) 9.0 cm+10.38 cm9.0 \mathrm{~cm}+10.38 \mathrm{~cm} b) 3.6 g/3 mL3.6 \mathrm{~g} / 3 \mathrm{~mL} c) 12.01 m×4.0 m12.01 \mathrm{~m} \times 4.0 \mathrm{~m} d) 59 mL58.38 mL59 \mathrm{~mL}-58.38 \mathrm{~mL} e) 24 g/2.02 mL24 \mathrm{~g} / 2.02 \mathrm{~mL} f) 10 cm×5.5 cm×18 cm10 \mathrm{~cm} \times 5.5 \mathrm{~cm} \times 18 \mathrm{~cm} g) (3.26×102)×(5.7×108)\left(3.26 \times 10^{-2}\right) \times\left(5.7 \times 10^{-8}\right) h) 2.34×103+5.6×1032.34 \times 10^{3}+5.6 \times 10^{3} i) 1.23×105÷4.5×1021.23 \times 10^{5} \div 4.5 \times 10^{-2}

Studdy Solution

STEP 1

Assumptions1. The calculations are to be performed as per the operations mentioned in the problem. . The results should be reported to the proper number of significant figures.
3. The units, when provided, should be included in the final answer.

STEP 2

For a), we are adding two measurements. The rule for addition and subtraction is that the result should have the same number of decimal places as the measurement with the least number of decimal places.
9.0cm+10.38cm9.0\, cm +10.38\, cm

STEP 3

Perform the addition.
19.38cm19.38\, cm

STEP 4

Round to the proper number of significant figures. In this case, we round to one decimal place because the measurement with the least number of decimal places (9.0 cm) has one decimal place.
19.4cm19.4\, cm

STEP 5

For b), we are dividing two measurements. The rule for multiplication and division is that the result should have the same number of significant figures as the measurement with the least number of significant figures.
3.g/3mL3.\, g /3\, mL

STEP 6

Perform the division.
1.2g/mL1.2\, g/mL

STEP 7

The result is already at the proper number of significant figures, so no rounding is needed.

STEP 8

For c), we are multiplying two measurements. The rule for multiplication and division is the same as in step5.
12.01m×4.0m12.01\, m \times4.0\, m

STEP 9

Perform the multiplication.
48.04m248.04\, m^2

STEP 10

Round to the proper number of significant figures. In this case, we round to two significant figures because the measurement with the least number of significant figures (4.0 m) has two significant figures.
48m248\, m^2

STEP 11

For d), we are subtracting two measurements. The rule for subtraction and addition is the same as in step.
59mL58.38mL59\, mL -58.38\, mL

STEP 12

Perform the subtraction.
0.62mL0.62\, mL

STEP 13

Round to the proper number of significant figures. In this case, we round to one decimal place because the measurement with the least number of decimal places (59 mL) has no decimal places.
0.6mL0.6\, mL

STEP 14

For e), we are dividing two measurements. The rule for division and multiplication is the same as in step.
24g/2.02mL24\, g /2.02\, mL

STEP 15

Perform the division.
11.881188118811881188118811881188g/mL11.881188118811881188118811881188\, g/mL

STEP 16

Round to the proper number of significant figures. In this case, we round to two significant figures because the measurement with the least number of significant figures (24 g) has two significant figures.
12g/mL12\, g/mL

STEP 17

For f), we are multiplying three measurements. The rule for multiplication and division is the same as in step5.
10cm×5.5cm×cm10\, cm \times5.5\, cm \times\, cm

STEP 18

Perform the multiplication.
990cm3990\, cm^3

STEP 19

The result is already at the proper number of significant figures, so no rounding is needed.

STEP 20

For g), we are multiplying two scientific notations. The rule for multiplication and division is the same as in step5.
(3.26×10)×(5.7×108)\left(3.26 \times10^{-}\right) \times \left(5.7 \times10^{-8}\right)

STEP 21

Perform the multiplication.
1.858×1091.858 \times10^{-9}

STEP 22

Round to the proper number of significant figures. In this case, we round to two significant figures because the measurement with the least number of significant figures (5.7 x10^-8) has two significant figures.
1.9×1091.9 \times10^{-9}

STEP 23

For h), we are adding two scientific notations. The rule for addition and subtraction is that the result should have the same number of decimal places as the measurement with the least number of decimal places.
.34×103+5.6×103.34 \times10^{3} +5.6 \times10^{3}

STEP 24

Perform the addition.
7.94×1037.94 \times10^{3}

STEP 25

Round to the proper number of significant figures. In this case, we round to two significant figures because the measurement with the least number of significant figures (5. x10^3) has two significant figures.
7.9×1037.9 \times10^{3}

STEP 26

For i), we are dividing two scientific notations. The rule for multiplication and division is the same as in step5.
1.23×105÷4.5×101.23 \times10^{5} \div4.5 \times10^{-}

STEP 27

Perform the division.
.7333333333333334×107.7333333333333334 \times10^{7}

STEP 28

Round to the proper number of significant figures. In this case, we round to three significant figures because the measurement with the least number of significant figures (1.23 x10^5) has three significant figures.
.73×107.73 \times10^{7}

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