Indicate if the following is true or false:
\sqrt{530} is an exact value.
\sqrt{324} is written in simplest exact form.
A calculator states that \sqrt{530} is 23.021728866. Is the decimal value exact?
Evaluate the following: \sqrt{56}. Round your answer to one decimal place.
Evaluate \sqrt{18} + \sqrt{41}. Round your answer to two decimal places.
Evaluate \sqrt{82}. Round your answer to three decimal places.
Use your calculator to find the approximate value of \sqrt{772} to the nearest tenth.
Round the following numbers as specified:
0.0829 to the nearest hundredth
\$723.817 to the nearest dollar
\$35.0486 to the nearest cent
Evaluate:
2.1 \times 5 \div 3 - 1.6
6.5 \times \left(7.8 + 1.6 - 6.4\right)
\left( 4.48 \div 2\right) \div \left( 0.8 \times 0.4\right)
Find the value of the following to three decimal places:
\left( - 4.3 \right)^{6}
- \left(8.4\right)^{4}
A satellite orbits the earth 10 times in 99 hours. How many hours does it take to complete 1 orbit? Write your answer as a decimal.
A farmer wants to have a square paddock with an area of 1000 \text{ m}^{2}. What would be the length of one side? Round your answer to two decimal places.
In competitive diving, seven judges score each dive. The lowest and highest scores are discounted, and the remaining five scores are averaged to give the diver's raw score.
Eileen achieved the following dive scores: 6.8, 7, 7.2, 7.1, 7.9, 6.9, 8.1
Find Eileen's raw score.
A diver's raw score is adjusted for its degree of difficulty, to become the diver's final score. Calculate Eileen's final score if the raw score is adjusted by being multiplied by 1.5.
State the number of significant figures in the following numbers:
10.20
0.00458
Round 0.006037736 to two significant figures.
Round 7231.0108 to five significant figures.
Consider the number 1083.
Round it to one significant figure.
Round it to two significant figures.
What is the difference between these two rounded values?
A nanometre (nm) is defined as being a billionth of a metre. This means that 1 \text{ nm} is 0.000000001 \text{ m}.
A germ has an approximate size of 1000 \text{ nm}. How many would fit in a 9 \text{ cm} sample?
Consider the following expression: 418 \text{ mL} \times 5.7\div934.5
How many significant figures does the least precise measurement have?
Calculate the result in milliliters, rounding your answer to the least number of significant figures from part (a).
Express the following numbers in scientific notation:
304\,000
0.973
Express nine hundred and five thousand and nine point one in scientific notation.
Write the basic numeral for 6 \times 10^{7}.
Write 8.87 \times 10^{ - 7 } in decimal notation.
For each set of numbers, state which one is the largest:
- 4.61 \times 10^{1}
- 1.19 \times 10^{1}
- 1.19 \times 10^{ - 6 }
- 8.99 \times 10^{ - 3 }
- 1.99 \times 10^{ - 6 }
- 8.99 \times 10^{ - 6 }
For each set of numbers, state which one is the smallest:
- 1.19 \times 10^{ - 6 }
- 4.61 \times 10^{1}
- 1.19 \times 10^{1}
- 1.99 \times 10^{ - 6 }
- 8.99 \times 10^{ - 6 }
- 8.99 \times 10^{ - 3 }
Use your calculator to find the value of
\frac{6702 \times 6424}{0.000088}
Write your answer in scientific notation, correct to five significant figures.
How many millimetres is that?
What is this when written using scientific notation?
A light year is defined as the distance that light can travel in one year. It is measured to be 9\,460\,730\,000\,000\,000 meters.
Write this using scientific notation.
How many kilometres is this? Write your answer in scientific notation.
How many centimetres is this? Write your answer in scientific notation.
Bone marrow in a person’s body produces 2.3 \times 10^{6} red blood cells each second.
Which of the following would be the closest rounded value for this number?
20 million each second
2 million each second
2 hundred thousand each second
Hence, estimate the number of red blood cells produced each minute.
The tiny tubes in our kidneys measure about 1.2 \times 10^{ - 5 } meters in diameter.
Which of the following would be the closest rounded value for this number?
1 ten-thousandth of a metre
1 millionth of a metre
1 hundred thousandth of a metre
Hence, estimate the diameter of the tubes in millimetres.
Use scientific notation and index laws to evaluate 11\,000\,000 \times 0.004 \times 0.0005 \times 20\,000. Leave your answer in scientific notation.
Evaluate 2.35 \times 10^{ - 7 } - 4.72 \times 10^{ - 8 }. Write your answer in scientific notation.
Evaluate 4.28 \times 10^{6} + 3.34 \times 10^{7}. Write your answer in scientific notation to three significant figures.
Evaluate: \frac{6.45 \times 10^{9} \times 4.3 \times 10^{ - 3 }}{8.3 \times 10^{4}}
Write your answer in scientific notation, correct to four decimal places.
Evaluate: 83\,000^{2} \times 79\,000\,000
Evaluate: 208 \times 10^{6} \div \left( 6.5 \times 10^{6}\right)