If x b + c = y c + a = z a + b then prove that b - c x + c - a y + a - b z = 0 .

Given: x b + c = y c + a = z a + b = k So, x = k b + c ; y = k c + a ; z = k a + b Consider L.H.S: b - c x + c - a y + a - b z = k b - c b + c + k c - a c + a + k a - b a + b = k b 2 - c 2 + c 2 - a 2 + a 2 - b 2 = k × 0 = 0 ∴ b - c x + c - a y + a - b z = 0 Hence, proved.

Match the columns in the following: Column A Column B (a) 1 decimetre (p) 1 1000 kilometer (b) 1 centimetre (q) 1 10 metre (c ) 1 millimetre (r) 1 100 metre (d) 1 metre (s) 1 1000 metre

We know that, 1 decimeter = 10 centimeters 10 centimeter = 0 .1 metre Thus, 1 dm = 0 .1 m = 1 10 m 1 metre = 100 centimetre Thus, 1 centimetre = 0 .01 m = 1 100 m . 1 metre = 1000 millimetres 1 mm = 1 1000 m Thus, 1 mm = 1 1000 m 1 kilometre = 1000 metres 1 m = 1 1000 km Thus, 1 m = 1 1000 km . Column A Column B (a) 1 decimetre (q) 1 10 metre (b) 1 centimetre (r) 1 100 metre (c ) 1 millimetre (s) 1 1000 metre (d) 1 metre (p) 1 1000 kilometer

Length of the nail — 2 c m and _____ m m or 2 . _____ c m .

Given, To find the length, measure using ruler. Length of nail = 2 c m 9 m m Now, 10 m m = 1 c m 1 m m = 1 10 c m 9 m m = 0.9 c m So, 2 c m 9 m m = 2.9 c m Therefore, length of nail is 2 . 9 cm .

Match the columns in the following: Column A Column B (a) 65 mm (p) 6500 cm (b) 65 km (q) 0 .65 m (c) 65 cm (r) 6 .5 cm (d) 65 m (s) 65000 m

We know that, 1 cm = 10 mm . 65 mm = 65 10 cm = 6 .5 cm , Thus, 65 mm = 6 .5 cm . 1 km = 1000 m . 65 km = 65 × 1000 m = 65000 m , Thus, 65 km = 65000 m . 1 cm = 1 100 m . 65 cm = 65 100 m = 0 .65 m Thus, 65 cm = 0 .65 m 1 m = 100 cm 65 m = 65 × 100 cm = 6500 cm Thus, 65 m = 6500 cm . Column A Column B (a) 65 mm (r) 6 .5 cm (b) 65 km (p) 6500 cm (c) 65 cm (q) 0 .65 m (d) 65 m (s) 65000 m Therefore, according the conversions the units are matched as shown above.

EASY

Earn 100

Solve the following problem.

Rafi said "the length of my finger nail is $5 cm$ and the length of my finger is $7 mm$ ". Is he correct? Give reasons.

Important Questions on Tenth and Hundredths

MEDIUM

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

A : B = 1 : 2, B : C = 3 : 2, & C : D = 1 : 3

, then the value of

A : B : C : D

EASY

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

\frac{x}{b + c} = \frac{y}{c + a} = \frac{z}{a + b}

then prove that

(b - c) x + (c - a) y + (a - b) z = 0

EASY

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

x : y = 2 : 3

and

y : z = 4 : 7

, then find

x : z

EASY

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

Express in millimetres.

$8 cm 9 mm =$

EASY

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

Express in terms of centimetres and millimetres.

$104 mm =$

EASY

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

$1 cm =$ _____ $mm$

EASY

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

Which unit will you use to measure?

The length of a belt.

Question Image

EASY

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

Express in terms of centimetres and millimetres.

$25 mm =$

MEDIUM

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

What was the length of the smallest pencil you have used? How long is this pencil? Guess ________ cm
Measure it using a scale.
How good is your guess?
We can see that Anju used a lens to make it look bigger.

Question Image

HARD

Mathematics>Arithmetic>Tenth and Hundredths>Measurement of Length

Match the columns in the following:

Column A	Column B
(a) $1 decimetre$	(p) $\frac{1}{1000} kilometer$
(b) $1 centimetre$	(q) $\frac{1}{10} metre$
(c ) $1 millimetre$	(r) $\frac{1}{100} metre$
(d) $1 metre$	(s) $\frac{1}{1000} metre$