14. Standard Form

Question 1

LEVEL 4

Write 97,864,532 into standard form.

Select the correct answer from the list below:

A: 9.7864532\times10^4

B: 9.7864532\times10^5

C: 9.7864532\times10^6

D: 9.7864532×10^7

CORRECT ANSWER:  D: 9.7864532×10^7

WORKED SOLUTION:

97,864,532=9.7864532×10^7 in standard form.

Question 2

LEVEL 4

Solve 888777 - 6556 and write your answer in standard form.

Select the correct answer from the options below:

A: 8.882221\times10^5

B: 8.882221\times10^6

C: 8.82221\times10^5

D: 8.82221×10^6

CORRECT ANSWER: C: 8.82221\times10^5

WORKED SOLUTION:

Answer = 888777 - 6556=882221=8.82221\times10^5

Question 3

LEVEL 4

Calculate 1476 + 32 in standard form.

Select the correct answer from the list below:

A: 1.508×10^2

B: 1.508×10^3

C: 1.508×10^4

D: 1.508×10^5

CORRECT ANSWER:  B: 1.508×10^3

WORKED SOLUTION:

Answer = 1476 + 32=1508=1.508\times10^3

Question 4

LEVEL 4

Solve 5,600,000\div800 and write the answer in standard form.

Select the correct answer from the list below:

A: 7\times10^3 

B: 7\times10^4

C: 7\times10^5 

D: 7\times10^6

CORRECT ANSWER: A: 7\times10^3

WORKED SOLUTION:

Write the numbers in standard a×10^n form i.e. 5.6×10^6 and 8×10^2

Divide 5.6 by 8: if the division is above 10 or below 1 then convert to a standard form and then proceed as follows.

(5.6\times10^6 )\div( 8\times10^2 )=(5.6\div8)\times( 10^6\div10^2)

Using the formula 10^a\div10^b=10^{a-b} to make number in standard form i.e. (5.6\div8)\times10^{6-2}=0.7\times10^4

Our number is below 1 so will need to convert it to standard form like this:

0.7\times10^4=7×10^{-1} \times10^4=7\times10^3

Answer: 5,600,000\div800=7×10^3 in standard form.

Answer = 7\times10^3

Question 5

LEVEL 4

Solve 0.85\times20 and write the answer in standard form.

Select the correct answer from the list below:

A: 1.7\times10^1

B: 1.7\times10^0

C: 1.7×10^{-1}

D: 1.7\times10^{-2}

CORRECT ANSWER:  A: 1.7\times10^1

WORKED SOLUTION:

Answer = 0.85\times20=1.7\times10^1