# Decimal Numbers Quiz Set 011

### Question 1

For what value of x would this expression be a perfect square: \$4.2 × 4.2 - x × 4.2 + 0.4 × 0.4\$?

A

0.8.

B

0.08.

C

0.008.

D

8.0.

Soln.
Ans: a

Comparing the given expression with \$a^2 - 2 × a ×b + b^2 = (a - b)^2\$, we see that if a = 4.2, and b = 0.4 then by inspection, x should be equal to 2b = 2 × 0.4 = 0.8.

### Question 2

What is \$8.958 - (-0.4) + 0.05 - (-0.08)\$?

A

9.488.

B

8.999.

C

8.975.

D

8.488.

Soln.
Ans: a

The given expression is same as \$8.958 + 0.4 + 0.05 + 0.08\$, then by simple addition we get \$8.958 + 0.4 + 0.05 + 0.08 = 9.488\$.

### Question 3

What is x in \$0.0098/x = 0.098\$?

A

0.1.

B

0.01.

C

1.0.

D

0.001.

Soln.
Ans: a

The expression becomes \$x = {98/98} × {1000/10000}\$ = 0.1.

### Question 4

What is \${0.50 × 0.50 × 0.50 + 0.06 × 0.06 × 0.06}/{4.50 × 4.50 × 4.50 + 0.54 × 0.54 × 0.54}\$?

A

\$1/9^3\$.

B

\$1/9^2\$.

C

\$1/9^4\$.

D

\$1/9\$.

Soln.
Ans: a

By inspection, the given ratio is same as \${0.50 × 0.50 × 0.50 + 0.06 × 0.06 × 0.06}/{9^3 × ({0.50 × 0.50 × 0.50 + 0.06 × 0.06 × 0.06})}\$ which is \$1/9^3\$.

### Question 5

What is \${2.50^2 - 2.26^2}/{2.50 - 2.26}\$?

A

+4.76.

B

0.024.

C

0.24.

D

-4.76.

Soln.
Ans: a

We know \$a^2 - b^2\$ = \$(a - b) × (a + b)\$. So \${a^2 - b^2}/{a - b}\$ is same as a + b. We get a + b = 2.50 + 2.26 = 4.76.