Decimal Fractions

Q1: The place value of 3 in 5.136 is

Step 1: Write the number clearly: 5.136Here,
– 1 is in the **tenths** place → \(\frac{1}{10}\)
– 3 is in the **hundredths** place → \(\frac{3}{100}\)
– 6 is in the **thousandths** place → \(\frac{6}{1000}\)
Step 2: So, the place value of 3 =

= \(\frac{3}{100}\)

Answer: c. \(\frac{3}{100}\)

Q2: The place value of 4 in 3.046 is

Step 1: Write the number clearly: 3.046 Step 2: Identify the decimal places: – 0 is in the tenths place → \(\frac{0}{10}\) – 4 is in the hundredths place → \(\frac{4}{100}\) – 6 is in the thousandths place → \(\frac{6}{1000}\)Step 3: So, the place value of 4 =

= \(\frac{4}{100}\)

Answer: d. \(\frac{4}{100}\)

Q3: \(3\frac{7}{10}=?\)

Step 1: Convert the mixed number to decimal. \[ 3\frac{7}{10} = 3 + \frac{7}{10} \]Step 2: Convert \(\frac{7}{10}\) into decimal: \[ \frac{7}{10} = 0.7 \]Step 3: Add: \[ 3 + 0.7 = 3.7 \]Answer: a. 3.7

Q4: 0.125 when expressed as a fraction in lowest terms is

Step 1: Write 0.125 as a fraction. \[ 0.125 = \frac{125}{1000} \]Step 2: Simplify the fraction: Divide numerator and denominator by 125 \[ \frac{125 \div 125}{1000 \div 125} = \frac{1}{8} \]Answer: b. \(\frac{1}{8}\)

Q5: 8 rupees 5 paise can be expressed as

Step 1: We know that: \[ 1\text{ rupee} = 100\text{ paise} \] So, \[ 5\text{ paise} = \frac{5}{100} = 0.05\text{ rupees} \]Step 2: Add to 8 rupees: \[ 8 + 0.05 = 8.05 \]Answer: c. ₹8.05

Q6: \(1 + 0.1 + 0.01 = ?\)

Step 1: Align decimal places and add:

   1.00
+  0.10
+  0.01
---------
   1.11

Step 2: Final result: \[ 1 + 0.1 + 0.01 = 1.11 \]Answer: b. 1.11

Q7: \(6\frac{19}{1000}=?\)

Step 1: Convert the mixed number to decimal: \[ 6\frac{19}{1000} = 6 + \frac{19}{1000} \]Step 2: Convert the fraction: \[ \frac{19}{1000} = 0.019 \]Step 3: Add: \[ 6 + 0.019 = 6.019 \]Answer: c. 6.019

Q8: 6.9, 5.4, 3.5 and 7.2 are

Step 1: Observe the decimal places of each number:
6.9 → 1 decimal place
5.4 → 1 decimal place
3.5 → 1 decimal place
7.2 → 1 decimal place
Step 2: Definition:
If all the decimals have the **same number of digits** after the decimal point, they are called **like decimals**.
Here, all numbers have **1 digit after decimal**, so they are **like decimals**.
Answer: a. like decimals

Q9: Which is greater 5.08 or 5.8?

Step 1: Align both numbers to compare:
5.08 = 5.080
5.8 = 5.800
Step 2: Compare digit by digit after the decimal point:
– Tenths: 0.0 vs 0.8 → 8 is greater
So clearly,
5.800 > 5.080
⇒ 5.8 > 5.08
Answer: b. 5.8

Q10: \(4.17+3.06+5.135=?\)

Step 1: Write all numbers with equal decimal places:
4.170
3.060
5.135
Step 2: Add them column-wise:

   4.170  
+  3.060  
+  5.135  
---------
  12.365

Answer: b. 12.365

Q11: 5 tenths when expressed as a decimal, is

Step 1: Understand the meaning of **5 tenths**: \[ \text{5 tenths} = \frac{5}{10} \]Step 2: Convert the fraction to decimal: \[ \frac{5}{10} = 0.5 \]Answer: a. 0.5

Q12: \(0.3 + 0.33 = ?\)

Step 1: Make decimal places equal by writing:

  0.30  
+ 0.33
 ------
  0.63

Step 2: Final addition result: \[ 0.3 + 0.33 = 0.63 \]Answer: c. 0.63

Q13: 6 km 225 m + 3 km 75 m = ?

Step 1: Convert metres into kilometre decimal:
225 m = \(\frac{225}{1000} = 0.225\) km
75 m = \(\frac{75}{1000} = 0.075\) km
Step 2: Write both values in decimal form:
6 km 225 m = 6.225 km
3 km 75 m = 3.075 km
Step 3: Add both:

  6.225  
+ 3.075
 -------
  9.300 km

Step 4: So expression becomes: (6.225 + 3.075) km
Answer: b. (6.225 + 3.075) km