Round the following answers off to a decimal places. $$ \begin{array}{ll} ext { (a) } \sqrt{8} & ext { (b) } \frac{3}{9} \ ext { c) } 2 \div 7 & ext { (d) } \sqrt[3]{96} \ ext { e) } 58 \div 89 & ext { () } \sqrt{77} \ ext { g) } 83 \div 11 & ext { (h) } \frac{15}{23} \ ext { i) } \sqrt[3]{72} & ext { i) } 14 \div 99\end{array} $$

Question

Round the following answers off to a decimal places. $$ \begin{array}{ll}	ext { (a) } \sqrt{8} & 	ext { (b) } \frac{3}{9} \ 	ext { c) } 2 \div 7 & 	ext { (d) } \sqrt[3]{96} \ 	ext { e) } 58 \div 89 & 	ext { () } \sqrt{77} \ 	ext { g) } 83 \div 11 & 	ext { (h) } \frac{15}{23} \ 	ext { i) } \sqrt[3]{72} & 	ext { i) } 14 \div 99\end{array} $$

UpStudy AI · Accepted Answer

Round the number by following steps:
- step0: Round $$\sqrt{77}$$ to $$2$$ decimal places using standard rounding method:
  $$\sqrt{77}$$
- step1: Rewrite in decimal:
  $$8.774964$$
- step2: Round $$8.774964$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$8.77$$
Round the number $$ 58 \div 89 $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$58 \div 89$$ to $$2$$ decimal places using standard rounding method:
  $$58 \div 89$$
- step1: Evaluate:
  $$58\div 89$$
- step2: Rewrite the expression:
  $$\frac{58}{89}$$
- step3: Rewrite in decimal:
  $$0.651685$$
- step4: Round $$0.651685$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$0.65$$
Round the number $$ 14 \div 99 $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$14 \div 99$$ to $$2$$ decimal places using standard rounding method:
  $$14 \div 99$$
- step1: Evaluate:
  $$14\div 99$$
- step2: Rewrite the expression:
  $$\frac{14}{99}$$
- step3: Rewrite in decimal:
  $$0.141414$$
- step4: Round $$0.141414$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$0.14$$
Round the number $$ \frac{15}{23} $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$\frac{15}{23}$$ to $$2$$ decimal places using standard rounding method:
  $$\frac{15}{23}$$
- step1: Rewrite in decimal:
  $$0.652174$$
- step2: Round $$0.652174$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$0.65$$
Round the number $$ \sqrt{8} $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$\sqrt{8}$$ to $$2$$ decimal places using standard rounding method:
  $$\sqrt{8}$$
- step1: Write as a product:
  $$\sqrt{4\times 2}$$
- step2: Write in exponential form:
  $$\sqrt{2^{2}\times 2}$$
- step3: Use the properties of radicals:
  $$\sqrt{2^{2}}\times \sqrt{2}$$
- step4: Simplify the root:
  $$2\sqrt{2}$$
- step5: Rewrite in decimal:
  $$2.828427$$
- step6: Round $$2.828427$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$2.83$$
Round the number $$ \frac{3}{9} $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$\frac{3}{9}$$ to $$2$$ decimal places using standard rounding method:
  $$\frac{3}{9}$$
- step1: Reduce the fraction:
  $$\frac{1}{3}$$
- step2: Rewrite in decimal:
  $$0.333333$$
- step3: Round $$0.333333$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$0.33$$
Round the number $$ 83 \div 11 $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$83 \div 11$$ to $$2$$ decimal places using standard rounding method:
  $$83 \div 11$$
- step1: Evaluate:
  $$83\div 11$$
- step2: Rewrite the expression:
  $$\frac{83}{11}$$
- step3: Rewrite in decimal:
  $$7.545455$$
- step4: Round $$7.545455$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$7.55$$
Round the number $$ 2 \div 7 $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$2 \div 7$$ to $$2$$ decimal places using standard rounding method:
  $$2 \div 7$$
- step1: Evaluate:
  $$2\div 7$$
- step2: Rewrite the expression:
  $$\frac{2}{7}$$
- step3: Rewrite in decimal:
  $$0.285714$$
- step4: Round $$0.285714$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$0.29$$
Round the number $$ \sqrt[3]{72} $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$\sqrt[3]{72}$$ to $$2$$ decimal places using standard rounding method:
  $$\sqrt[3]{72}$$
- step1: Write as a product:
  $$\sqrt[3]{8\times 9}$$
- step2: Write in exponential form:
  $$\sqrt[3]{2^{3}\times 9}$$
- step3: Use the properties of radicals:
  $$\sqrt[3]{2^{3}}\times \sqrt[3]{9}$$
- step4: Simplify the root:
  $$2\sqrt[3]{9}$$
- step5: Rewrite in decimal:
  $$4.160168$$
- step6: Round $$4.160168$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$4.16$$
Round the number $$ \sqrt[3]{96} $$ into 2 decimal places.
Round the number by following steps:
- step0: Round $$\sqrt[3]{96}$$ to $$2$$ decimal places using standard rounding method:
  $$\sqrt[3]{96}$$
- step1: Write as a product:
  $$\sqrt[3]{8\times 12}$$
- step2: Write in exponential form:
  $$\sqrt[3]{2^{3}\times 12}$$
- step3: Use the properties of radicals:
  $$\sqrt[3]{2^{3}}\times \sqrt[3]{12}$$
- step4: Simplify the root:
  $$2\sqrt[3]{12}$$
- step5: Rewrite in decimal:
  $$4.578857$$
- step6: Round $$4.578857$$ to $$2$$ decimal places using standard rounding method$$:$$
  $$4.58$$
Here are the rounded answers to two decimal places:

$$
\begin{array}{ll}
\text{(a) } \sqrt{8} & \approx 2.83 \
\text{(b) } \frac{3}{9} & \approx 0.33 \
\text{(c) } 2 \div 7 & \approx 0.29 \
\text{(d) } \sqrt[3]{96} & \approx 4.58 \
\text{(e) } 58 \div 89 & \approx 0.65 \
\text{(f) } \sqrt{77} & \approx 8.77 \
\text{(g) } 83 \div 11 & \approx 7.55 \
\text{(h) } \frac{15}{23} & \approx 0.65 \
\text{(i) } \sqrt[3]{72} & \approx 4.16 \
\text{(j) } 14 \div 99 & \approx 0.14 \
\end{array}
$$
Here are the rounded answers to two decimal places: $$ \begin{array}{ll} \text{(a) } \sqrt{8} & \approx 2.83 \ \text{(b) } \frac{3}{9} & \approx 0.33 \ \text{(c) } 2 \div 7 & \approx 0.29 \ \text{(d) } \sqrt[3]{96} & \approx 4.58 \ \text{(e) } 58 \div 89 & \approx 0.65 \ \text{(f) } \sqrt{77} & \approx 8.77 \ \text{(g) } 83 \div 11 & \approx 7.55 \ \text{(h) } \frac{15}{23} & \approx 0.65 \ \text{(i) } \sqrt[3]{72} & \approx 4.16 \ \text{(j) } 14 \div 99 & \approx 0.14 \ \end{array} $$

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