Q: Express as \$kg\$ using decimals.\$26\ kg\$ and \$50\ g\$

As \$1000g=1\ kg\$ \$\implies 1g=\dfrac{1}{1000}\ kg\$.\$26\ kg\ 50\ g\$.\$=26\ kg+50\ g\$\$=26\ kg+50\left(\dfrac{1}{1000}\right) kg\$.\$=26+0.05\ kg\$.\$=26.05\ kg\$.

Q: Express as \$km\$ using decimals.\$70\ km\$ and \$5\ m\$

\$70\ km\ 5\ m\$\$=70\ km+5\ m\$\$=70\ km+5\times 1\ m\$\$=70\ km+5\left(\dfrac{1}{1000}\right)\ km\$ ........ As \$1000m=1\ km\$\$=70\ km+0.005\ km\$\$=70.005\ km\$

Q: Convert the following into metres and centimetres.\$673\ \text{cm}\$

We know that\$1\$ \$\text{meter} =100\$ \$\text{cm}\$\$1\$ \$\text{cm} =\dfrac1{100}\$ \$\text{m}\$\$673\$ \$\text{cm} =\dfrac1{100} \times 673\$ \$\text{m}\$ \$=\dfrac{673}{100} \$ \$\text{m}\$ \$= 6.73 ~ \text{m}\$It is equivalent to \$6\$ \$\text{m}\$ and \$73\$ \$\text{cm}\$So, Option \$\text{A}\$ is correct

Q: Express in meters using decimals.\$9\ m\$ and \$7\ cm\$

\$9m\$ & \$7cm\$\$9m+7\left(\dfrac{1}{100}\right)m\$ ........... As\$100\ cm=1\ m\$\$9m+0.07m\$\$=9.07m\$

Q: A train \$280 m\$ long, running with a speed of 63\$\mathrm { km } /\$ hr will pass a tree in

\$Speed\>of\>train\>=\>63(\dfrac{Km}{hr})\\=(\dfrac{63\cdot100m}{3600s})\\=17.5(\dfrac{m}{s})\\By\>passing\>a\>tree,\>train\>will\>have\>to\>cross\>its\>own\>length\\\therefore\>Time\>taken\>=\>(\dfrac{280}{17.5})=16sec\$

Q: Express as \$km\$ using decimals.\$8\ m\$

\$8m\$As \$1000m=1km\$\$1m=\dfrac{1}{1000}km\$\$8m=8\times 1m\$\$=8\times\dfrac{1}{1000}km\$\$=0.008km\$

Q: What comes after 10 crore in Indian system?

As per the Indian system after \$10\$ crores, we get the \$100\$ crores. In the International system, which is equal to \$1\$ billion and is numerically represented as \$109\$.To find the value after \$10\$ crores in the Indian system, let us recall all the values starting from \$1\$.Number Value\$1\$ One\$10 \$ Ten\$100\$ Hundred\$1000\$ Thousand\$10000\$ Ten thousand \$100000\$ One lakh\$1000000\$ Ten Lakhs\$10000000\$ One crore\$100000000\$ Ten crores\$1000000000\$ Arab\$10000000000\$ Ten Arab\$100000000000\$ One Kharab\$1000000000000\$ Ten Kharab

Q: Express as \$km\$ using decimals.\$88\ m\$

\$88m\$As \$1000m=1km\$\$1m=\dfrac{1}{1000}km\$\$=88\times 1m\$\$=88\times\dfrac{1}{1000}km\$\$=0.088km\$

Q: The value of 50 coins of 50 paisa = Rs_____

The value of \$ 50 \$ coins of \$ 50 \$ paisa = Rs \$ 25 \$\$ 50 \times 50 = 2500 paisa \$\$ \Rightarrow Rs \dfrac {2500}{100} = Rs \dfrac { 2500 \div 100}{ 100 \div 100} = Rs 25 \$

Q: Express the ratio in its simplest form \$200m: 5km\$

\$(\frac{200m}{5Km})\\=(\frac{200m}{5\times 1000m})\\=(\frac{1}{25})\\or \>1:25\$

Question 1

Express as $kg$ using decimals.$26\ kg$ and $50\ g$

Accepted Answer

As $1000g=1\ kg$ $\implies 1g=\dfrac{1}{1000}\ kg$.$26\ kg\ 50\ g$.$=26\ kg+50\ g$$=26\ kg+50\left(\dfrac{1}{1000}\right) kg$.$=26+0.05\ kg$.$=26.05\ kg$.

Question 2

Express as $km$ using decimals.$70\ km$ and $5\ m$

Accepted Answer

$70\ km\ 5\ m$$=70\ km+5\ m$$=70\ km+5\times 1\ m$$=70\ km+5\left(\dfrac{1}{1000}\right)\ km$  ........ As $1000m=1\ km$$=70\ km+0.005\ km$$=70.005\ km$

Question 3

Convert the following into metres and centimetres.$673\ \text{cm}$

Accepted Answer

We know that$1$  $\text{meter} =100$  $\text{cm}$$1$  $\text{cm} =\dfrac1{100}$  $\text{m}$$673$  $\text{cm} =\dfrac1{100} \times 673$  $\text{m}$                $=\dfrac{673}{100}   $  $\text{m}$                 $= 6.73 ~ \text{m}$It is equivalent to $6$ $\text{m}$ and $73$ $\text{cm}$So, Option $\text{A}$ is correct

Question 4

Express in meters using decimals.$9\ m$ and $7\ cm$

Accepted Answer

$9m$  &  $7cm$$9m+7\left(\dfrac{1}{100}\right)m$   ...........  As$100\ cm=1\ m$$9m+0.07m$$=9.07m$

Question 5

A train $280 m$ long, running with a speed of 63$\mathrm { km } /$ hr will pass a tree in

Accepted Answer

$Speed\>of\>train\>=\>63(\dfrac{Km}{hr})\=(\dfrac{63\cdot100m}{3600s})\=17.5(\dfrac{m}{s})\By\>passing\>a\>tree,\>train\>will\>have\>to\>cross\>its\>own\>length\\therefore\>Time\>taken\>=\>(\dfrac{280}{17.5})=16sec$

Question 6

Express as $km$ using decimals.$8\ m$

Accepted Answer

$8m$As $1000m=1km$$1m=\dfrac{1}{1000}km$$8m=8\times 1m$$=8\times\dfrac{1}{1000}km$$=0.008km$

Question 7

What comes after 10 crore in Indian system?

Accepted Answer

As per the Indian system after $10$ crores, we get the $100$ crores. In the International system, which is equal to $1$ billion and is numerically represented as $109$.To find the value after $10$ crores in the Indian system, let us recall all the values starting from $1$.Number                                  Value$1$                                               One$10 $                                            Ten$100$                                          Hundred$1000$                                        Thousand$10000$                                      Ten thousand $100000$                                    One lakh$1000000$                                  Ten Lakhs$10000000$                                One crore$100000000$                              Ten crores$1000000000$                            Arab$10000000000$                         Ten Arab$100000000000$                       One Kharab$1000000000000$                     Ten Kharab

Question 8

Express as $km$ using decimals.$88\ m$

Accepted Answer

$88m$As $1000m=1km$$1m=\dfrac{1}{1000}km$$=88\times 1m$$=88\times\dfrac{1}{1000}km$$=0.088km$

Question 9

The value of 50 coins of 50 paisa = Rs_____

Accepted Answer

The value of $ 50 $ coins of $ 50 $ paisa = Rs $ 25 $$ 50 \times 50 = 2500 paisa $$ \Rightarrow Rs \dfrac {2500}{100} =  Rs  \dfrac  { 2500 \div  100}{ 100 \div  100} = Rs 25 $

Question 10

Express the ratio in its simplest form $200m: 5km$

Accepted Answer

$(\frac{200m}{5Km})\=(\frac{200m}{5\times 1000m})\=(\frac{1}{25})\or \>1:25$