# Decimal Numbers Quiz Set 016

### Question 1

Which is the smallest?

A

\$0.3^3\$.

B

\$1/0.3\$.

C

\$0.3\$.

D

\$0.3^2\$.

Soln.
Ans: a

We know that if a number is less than 1, then it becomes smaller and smaller as it is raised to higher and higher positive powers. Now, \$1/0.3\$ is same as \$0.3^{-1}\$. The three powers of 0.3 given to us are -1, 1, 2 and 3. Out of these 3 is the most positive, so, \$0.3^3\$ is the smallest.

### Question 2

What is \${88 × 6.6 - 68 × 6.3}/1.3\$?

A

\$117{3/13}\$.

B

\$117{1/13}\$.

C

\$117{5/13}\$.

D

\$117{7/13}\$.

Soln.
Ans: a

Observe that all fractional numbers are having one digit to the right of the dot. So we can cancel all the dots and get a plain expression: \${88 × 66 - 68 × 63}/13\$ which equals \${1524/13}\$, which is same as: \$117{3/13}\$

### Question 3

For what value of x would this expression be a perfect square: \$9.74 × 9.74 + x × 9.74 + 0.3 × 0.3\$?

A

0.6.

B

0.06.

C

0.006.

D

6.0.

Soln.
Ans: a

Comparing the given expression with \$a^2 + 2 × a ×b + b^2 = (a + b)^2\$, we see that if a = 9.74, and b = 0.3 then by inspection, x should be equal to 2b = 2 × 0.3 = 0.6.

### Question 4

What is x in \$0.008/x = 10\$?

A

0.0008.

B

0.008..

C

0.08..

D

0.00008..

Soln.
Ans: a

The expression becomes \$x = {8/1000} × {1/10}\$ = 0.0008.

### Question 5

What is 0.0027 × 0.04?

A

\$1.08 × 10^{-4}\$.

B

\$1.08 × 10^{-3}\$.

C

\$1.08 × 10^{-2}\$.

D

\$1.08 × 10^{-5}\$.

Soln.
Ans: a 